Flips and abundance for algebraic threefolds - A summer seminar at the University of Utah (Salt Lake City, 1991)

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Avec les contributions de : Abramovich, Dan ; Alexeev, Valery ; Corti, Alessio ; Fong, Lung-Ying ; Grassi, Antonella ; Keel, Sean ; Luo, Tie ; Matsuki, Kenji ; Kollár, János ; Megyesi, Gábor ; McKernan, James ; Morrison, David R. ; Paranjape, Kapil H. ; Shepherd-Barron, Nicholas I. ; Srinivas, Vasudevan

Astérisque, no. 211 (1992) , 268 p.

Voir la notice du livre provenant de la source Numdam

Zbl

@book{AST_1992__211__1_0,
     editor = {Koll\'ar, J\'anos},
     title = {Flips and abundance for algebraic threefolds - {A} summer seminar at the {University} of {Utah} {(Salt} {Lake} {City,} 1991)},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {211},
     year = {1992},
     zbl = {0782.00075},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/AST_1992__211__1_0/}
}

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%E Kollár, János
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Kollár, János (éd.). Flips and abundance for algebraic threefolds - A summer seminar at the University of Utah (Salt Lake City, 1991). Astérisque, no. 211 (1992), 268 p. https://geodesic-test.mathdoc.fr/item/AST_1992__211__1_0/

Bibliographie
Cité par

[Alexeev89] V. A. Alexeev, Fractional indices of log Del Pezzo surfaces, Math. USSR Izv. 8 (1989), 613-629. | MR | Zbl

[Alexeev92] V. A. Alexeev, General elephants for Mori fiber spaces, (to appear), Compositio Math.

[Artin62] M. Artin, Some numerical criteria for contractibility of curves on algebraic surfaces, Amer.J.Math. 84 (1962), 485-496. | MR | Zbl | DOI

[Artin66] M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), 129-137. | MR | Zbl | DOI

[Artin70] M. Artin, Algebraisation of formal moduli II, Ann. of Math. 91 (1970), 88-135. | MR | Zbl | DOI

[Artin74] M. Artin, Algebraic construction of Brieskorn's resolutions, J. Alg. 29 (1974), 330-348. | MR | Zbl | DOI

[Artin86] M. Artin, Néron models, arithmetic geometry (G. Cornell and J. Silverman eds.), Springer Verlag, 1986, pp. 213-230. | MR | Zbl | DOI

[BPV84] W. Barth - C. Peters - A. Van De Ven, Compact complex surfaces, Springer, 1984. | MR | Zbl | DOI

[Bogomolov79] F. A. Bogomolov, Holomorphic tensors and vector bundles on projective varieties, Math. U.S.S.R. Izvestiya 13 (1979), 499-555. | Zbl | DOI

[Brieskorn68] E. Brieskorn, Rationale Singularitäten komplexer Flächen, Invent. Math. 4 (1968), 336-358. | MR | Zbl | EuDML | DOI

[Brieskorn71] E. Brieskorn, Singular elements of semisimple algebraic groups, Proc. Int. Congr. Math. Nice, Gauthier-Villars, 1971, pp. 279-284. | MR | Zbl

[CKM88] H. Clemens - J. Kollár - S. Mori, Higher dimensional complex geometry, Astérisque vol. 166, Soc. Math. France, 1988. | Zbl | mathdoc-id | MR

[Corti92] A. Corti, Families of Del Pezzo Surfaces (thesis) University of Utah.

[Cutkosky88] S. D. Cutkosky, Weil divisors and symbolic algebras, Duke Math. J. 57 (1988), 175-183. | Zbl | MR | DOI

[Deligne71] P. Deligne, Théorie de Hodge, II, Publ. Math. I.H.E.S. 40 (1971), 5-57. | MR | Zbl | EuDML | mathdoc-id | DOI

[Donaldson85] S. Donaldson, Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. Lond. Math. Soc. 50 (1985), 1-26. | MR | Zbl | DOI

[DuBois81] Ph. Du Bois, Complex de de Rham filtré d'une variété singulière, Bull. Soc. Math. France 109 (1981), 41-81. | MR | Zbl | EuDML | mathdoc-id | DOI

[Ekedahl87] T. Ekedahl, Foliations and inseparable morphisms, Algebraic Geometry, Bowdoin, Proc. Symp. Pure Math. 46, S. Bloch ed., A.M.S. Providence, 1987, pp. 139-149. | MR | Zbl

[Fujita84] T. Fujita, Fractionally logarithmic canonical rings of surfaces, J. Fac. Sci. Tokyo Univ. 30 (1984), 685-696. | MR | Zbl

[Fulton75] W. Fulton, Rational equivalence on singular varieties, Publ. Math. I.H.E.S. 45 (1975), 147-167. | MR | Zbl | EuDML | mathdoc-id | DOI

[Fulton84] W. Fulton, Intersection theory, Springer, 1984. | MR | Zbl | DOI

[Friedman-Morrison83] R. Friedman - D. Morrison, The birational geometry of degenerations: an overview, The birational geometry of degenerations, Progress in Math. vol. 29, Birkhäuser, 1983, pp. 1-32. | MR | Zbl

[Grassi91] A. Grassi, On minimal models of elliptic threefolds, Math. Ann. 290 (1991), 287-301. | MR | Zbl | EuDML | DOI

[Griffiths-Schmid73] P. Griffiths - W. Schmid, Recent developments in Hodge theory, discrete subgroups of Lie groups, Oxford Univ. Press, 1973, pp. 31-127. | MR | Zbl

[Grothendieck62] A. Grothendieck, Fondements de géométrie algébrique, Sec. Math. Paris, 1962. | Zbl

[Grothendieck66] A. Grothendieck, On the de Rham cohomology of algebraic varieties, Publ. Math. IHES 29 (1966), 95-103. | MR | Zbl | EuDML | mathdoc-id | DOI

[Grothendieck68] A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux - SGA 2, North Holland, 1968. | MR | Zbl

[Hartshorne66] R. Hartshorne, Residues and duality, Springer Lecture Notes vol. 20, 1966. | MR | Zbl | EuDML

[Hartshorne77] R. Hartshorne, Algebraic geometry, Springer, 1977. | MR | Zbl | DOI

[Hodge-Pedoe52] W. Hodge - D. Pedoe, Methods of algebraic geometry, Cambridge Univ. Press, 1952. | Zbl | MR

[Iliev86] A. I. Iliev, Log terminal singularities of algebraic surfaces, Moscow Univ.Bull. 41, no.3 (1986), 38-44. | MR | Zbl

[Ishii85] S. Ishii, On isolated Gorenstein singularities, Math. Ann. 270 (1985), 541-554. | MR | Zbl | EuDML | DOI

[Iskovskikh87] V. A. Iskovskikh, On the rationality problem for conic bundles, Duke Math. J. 54 (1987), 271-294. | MR | Zbl | DOI

[Kawamata79] Y. Kawamata, On the classification of open algebraic surfaces, Algebraic Geometry, Copenhagen, Springer Lecture Notes vol. 732, 1979, pp. 215-233. | MR | Zbl

[Kawamata84a] Y. Kawamata, On the finiteness of generators of the pluri-canonical ring for a threefold of general type, Amer. J. Math. 106 (1984), 1503-1512. | MR | Zbl | DOI

[Kawamata84b] Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. | MR | Zbl | DOI

[Kawamata85] Y. Kawamata, Pluricanonical systems on minimal algebraic varieties, Inv. Math. 79 (1985), 567-588. | MR | Zbl | EuDML | DOI

[Kawamata88] Y. Kawamata, The crepant blowing-up of $3$ -dimensional canonical singularities and its application to the degeneration of surfaces, Ann. of Math 127 (1988), 93-163. | MR | Zbl | DOI

[Kawamata91a] Y. Kawamata, Boundedness of $ℚ$ -Fano threefolds, Proc. Int. Conf. Algebra, vol. 131, Contemp. Math., 1992, pp. 439-445. | MR | Zbl

[Kawamata91b] Y. Kawamata, Abundance Theorem for Minimal Three-folds, Inv. Math. 108 (1992), 229-246. | MR | Zbl | EuDML | DOI

[Kawamata91c] Y. Kawamata, Termination of Log Flips for Algebraic $3$ -Folds, Internat. J. Math. 3 (1992), 653-660. | MR | Zbl | DOI

[Kawamata91d] Y. Kawamata, Log Canonical Models of Algebraic $3$ -Folds, Internat. J. Math. 3 (1992), 351-357. | MR | Zbl | DOI

[KMM87] Y. Kawamata - K. Matsuda - K. Matsuki, Introduction to the Minimal Model Problem, Algebraic Geometry, Sendai, Adv. Stud. Pure Math, vol 10. T. Oda ed., Kinokuniya - North-Holland, 1987, pp. 283-360. | MR | Zbl | DOI

[Kobayashi90] R. Kobayashi, Uniformization of complex surfaces, Adv. Stud. Pure. Math., vol. 18-2, Kinokuniya, 1990, pp. 313-394. | MR | Zbl | DOI

[KNS89] R. Kobayashi - S. Nakamura - F. Sakai, A numerical characterisation of ball quotients for normal surfaces with branch loci, Proc. Japan Acad. Sci. 65 (1989), 238-241. | MR | Zbl | DOI

[Kollár87] J. Kollár, The structure of algebraic threefolds - an introduction to Mori's program, Bull. AMS 17 (1987), 211-273. | MR | Zbl | DOI

[Kollár89] J. Kollár, Flops, Nagoya Math. J. 113 (1989), 14-36. | MR | Zbl | DOI

[Kollár90] J. Kollár, Minimal Models of Algebraic Threefolds: Mori's Program, Asterisque 177-178 (1990), 303-326. | MR | Zbl | EuDML | mathdoc-id

[Kollár91] J. Kollár, Flips, Flops, Minimal Models, etc., Surv. in Diff. Geom. 1 (1991), 113-199. | MR | Zbl

[Kollár-Mori92] J. Kollár - S. Mori, Classification of three dimensional flips, Jour. AMS 5 (1995), 533-703. | MR | Zbl

[KSB88] J. Kollár - N. Shepherd-Barron, Threefolds and deformations of surface singularities, Inv. Math. 91 (1988), 299-338. | MR | Zbl | EuDML | DOI

[Lange-Stuhler77] H. Lange - U. Stuhler, Vectorbündel auf Kurven und Darstellungen der algebraischer Fundamentalgruppe, Math. Z. 156 (1977), 73-83. | MR | Zbl | EuDML | DOI

[Laufer77] H. Laufer, On minimally elliptic singularities, Am. J. Math. 99 (1977), 1257-1295. | MR | Zbl | DOI

[Markushevich85] D. G. Markushevich, Canonical singularities of three dimensional hypersurfaces, Izv. AN SSSR 49 (1995), 334-368. | MR | Zbl

[Matsuki90] K. Matsuki, An approach to the abundance conjecture for three-folds, Duke Math. J. 61 (1990), 207-220. | MR | Zbl | DOI

[Matsuki91] K. Matsuki, Termination of flops for $4$ -folds, Amer. J. Math. 113 (1991), 835-860. | MR | Zbl | DOI

[Mehta-Ramanathan82] V. B. Mehta - A. Ramanathan, Semistable sheaves on projective varieties and their restriction to curves, Math. Ann. 258 (1982), 213-224. | MR | Zbl | EuDML | DOI

[Mehta-Ramanathan84] V. B. Mehta - A. Ramanathan, Restriction of stable sheaves and representations of the fundamental group, Inv. Math. 77 (1984), 163-172. | MR | Zbl | EuDML | DOI

[Milnor68] J. Milnor, Singular Points of Complex Hypersurfaces, Annals of Mathematics Studies, Number 61, Princeton University Press, Princeton, New Jersey, 1968. | MR | Zbl

[Miyaoka77] Y. Miyaoka, On Chern numbers of surfaces of general type, Invent. Math. 42 (1977), 225-237. | MR | Zbl | EuDML | DOI

[Miyaoka84] Y. Miyaoka, The maximal number of quotient singularities on surfaces with given numerical invariants, Math. Ann. 268 (1984), 159-171. | MR | Zbl | EuDML | DOI

[Miyaoka87a] Y. Miyaoka, Deformation of a morphism along a foliation, Algebraic Geometry Bowdoin 1985, Proc. Symp. Pure Math. vol. 46, 1987, pp. 245-268. | MR | Zbl

[Miyaoka87b] Y. Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, Advanced Studies in Pure Math. 10, Algebraic Geometry Sendai 85, Kinokuniya-North Holland, 1987, pp. 449-476. | MR | Zbl | DOI

[Miyaoka88a] Y. Miyaoka, On the Kodaira dimension of minimal threefolds, Math. Ann. 281 (1988), 325-332. | MR | Zbl | EuDML | DOI

[Miyaoka88b] Y. Miyaoka, Abundance conjecture for threefolds: $υ = 1$ case, Comp. Math. 68 (1988), 203-220. | Zbl | EuDML | mathdoc-id | MR

[Miyaoka91] Y. Miyaoka, Theme and variations - inequalities between Chern numbers, Sugaku Translations 4 (1991), 157-176. | MR | Zbl

[Miyaoka-Mori86] Y. Miyaoka - S. Mori, A numerical criterion for uniruledness, Ann. of Math. 124 (1986), 65-69. | MR | Zbl | DOI

[Mori82] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133-176. | MR | Zbl | DOI

[Mori87] S. Mori, Classification of higher-dimensional varieties, Algebraic Geometry Bowdoin 1985, Proc. Symp. Pure Math. vol. 46, 1987, pp. 269-332. | MR | Zbl | DOI

[Mori88] S. Mori, Flip theorem and the existence of minimal models for $3$ -folds, Journal AMS 1 (1988), 117-253. | MR | Zbl

[Morin40] U. Morin, Sull' unirazionalità dell' ipersuperficie algebrica di qualunque ordine e dimensione sufficientemente alta, Atti dell II Congresso Unione Math. Ital., 1940, pp. 298-302. | MR | JFM

[Mumford61] D. Mumford, The topology of an algebraic surface and a criterion for simplicity, Publications IHES 9 (1961), 5-22. | MR | Zbl | EuDML | mathdoc-id | DOI

[Mumford83] D. Mumford, Towards an enumerative geometry of the moduli space of curves, Arithmetic and Geometry, Papers Dedicated to I. R. Shafarevich on the Occasion of His Sixtieth Birthday, Volume II, Geometry, M. Artin and J. Tate, eds., Birkhäuser, Boston - Basel - Stuttgart, 1983, pp. 271-328. | MR | Zbl

[Nakayama88] N. Nakayama, The singularities of the canonical model of complex Kähler manifolds, Math. Ann. 280 (1988), 509-512. | MR | Zbl | EuDML | DOI

[Predonzan48] A. Predonzan, Intorno agli $S_{k}$ giacenti sulla varietà intersezione completa di più forme, Rend. Acc. Lincei 5 (1948), 238-242. | MR | Zbl

[Predonzan49] A. Predonzan, Sull' unirazionalità della varietà intersezione completa di più forme, Rend. Sem. Mat. Padova 18 (1949), 163-176. | MR | Zbl | EuDML | mathdoc-id

[Ramero90] L. Ramero, Effective bounds for unirationality of complete intersections, Manu. Math. 68 (1990), 435-445. | MR | Zbl | EuDML

[Reid75] M. Reid, Elliptic Gorenstein singularities of surfaces, (unpublished ms.) Univ. of Warwick (1975).

[Reid80] M. Reid, Canonical $3$ -folds, Geometrie Algébrique Angers, A. Beauville ed., Sijthoff & Noordhoff, 1980, pp. 273-310. | MR | Zbl

[Reid83] M. Reid, Minimal models of canonical threefolds, Algebraic Varieties and Analytic Varieties, Adv. Stud. Pure Math. vol 1. S. Iitaka ed., Kinokuniya and North-Holland, 1983, pp. 131-180. | MR | Zbl

[Reid87] M. Reid, Young person's guide to canonical singularities, Algebraic Geometry Bowdoin 1985, Proc. Symp. Pure Math. vol. 46, 1987, pp. 345-416. | MR | Zbl | DOI

[Roth55] L. Roth, Algebraic Threefolds, Springer Verlag, Berlin - Göttingen - Heidelberg, 1955. | MR | Zbl

[Sakai80] F. Sakai, Semi-stable curves on algebraic surfaces and logarithmic pluricanonical maps, Math. Ann. 254 (1980), 89-120. | MR | Zbl | EuDML | DOI

[Sakai83] F. Sakai, $D$ -dimensions of algebraic surfaces and numerically effective divisors, Comp. Math. 48 (1983), 101-118. | MR | Zbl | EuDML | mathdoc-id

[Sakai87] F. Sakai, Classification of normal surfaces, Algebraic Geometry, Bowdoin, Proc. Symp. Pure Math. 46, S. Bloch ed., A.M.S. Providence, 1987, pp. 451-466. | MR | Zbl

[Sarkisov81] V. G. Sarkisov, Birational automorphisms of conic bundles, Math. USSR Izv. 17 (1981), 177-202. | Zbl | DOI

[Sarkisov82] V. G. Sarkisov, On the structure of conic bundles, Math. USSR Izv. 120 (1982), 355-390. | Zbl

[Seshadri82] C. S. Seshadri, Fibres vectoriels sur les courbes algébriques, Astérisque vol. 96, Soc. Math. France, 1982. | MR | Zbl | mathdoc-id

[Shepherd-Barron91] N. I. Shepherd-Barron, Unstable vector bundles and linear systems on surfaces in char. p, Invent. Math. (1992), 214-233. | MR | Zbl

[Shokurov85] V. V. Shokurov, The nonvanishing theorem, Izv. A. N. SSSR Ser. Mat. 49 (1985), 635-651 | MR | Zbl

V. V. Shokurov, The nonvanishing theorem, Math. USSR. Izv. 19 (1985), 591-604. | Zbl

[Shokurov88] V. V. Shokurov, Problems about Fano varieties, Birational Geometry of Algebraic Varieties, Open Problems, 1988, pp. 30-32.

[Shokurov91] V. V. Shokurov, $3$ -fold log flips, (in Russian), Izv. A. N. Ser. Mat. 56 (1992), 105-203. | Zbl

[Shokurov92] V. V. Shokurov, Addition to " $3$ -fold log flips", (in Russian, to appear), Izv. A. N. Ser. Mat. 57 (1993). | Zbl

[Shokurov93] V. V. Shokurov, 3-fold log flips, (revised translation of [Shokurov91 and 92], with commentaries by M. Reid), Izv. A. N. Ser. Mat. 56 (1993). | Zbl

[Siu87] Y.-T. Siu, Lectures on Hermitian-Einstein metrics for stable bundles and Kähler-Einstein metrics, DMV Seminar vol. 8, Birkhäuser, 1987. | MR | Zbl

[Steenbrink83] J. H. M. Steenbrink, Mixed Hodge structures associated with isolated singularities, Singularities - Part 2, Proc. Symp. Pure Math vol. 40, 1983, pp. 513-536. | MR | Zbl | DOI

[Stevens88] J. Stevens, On canonical singularities as total spaces of deformations, Abh. Math. Sem. Univ. Hamburg 58 (1988), 275-283.

[vanStraten87] D. Van Straten, Weakly normal surface singularities and their improvements, (thesis), Leiden (1987).

[Ueno82] K. Ueno, Bimeromorphic geometry of algebraic and analytic three-folds, Algebraic Threefolds, Lecture Notes in Mathematics 947, A. Conte ed., Springer, 1982, pp. 1-34.

[Viehweg80] E. Viehweg, Klassifikationstheorie algebraischer Varietäten der Dimension drei, Comp. Math. 41 (1980), 361-400.

[Yau77] S.-T. Yau, Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. 74 (1977), 1798-1799.