Minimal resolution of general stable rank-2 vector bundles on ${\mathbb{P}}^2$

Dionisi, Carla ; Maggesi, Marco

Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 1, pp. 151-160.

Abstract (VO)

We study general elements of moduli spaces ${\mathfrak{M}}_{{\mathbb{P}}^2}(2,c_1,c_2)$ of rank-2 stable holomorphic vector bundles on ${\mathbb{P}}^2$ and their minimal free resolutions. Incidentally, a quite easy proof of the irreducibility of ${\mathfrak{M}}_{{\mathbb{P}}^2}(2,c_1,c_2)$ is shown.

Riassunto

Abbiamo studiato gli elementi generici degli spazi di moduli ${\mathfrak{M}}_{{\mathbb{P}}^2}(2,c_1,c_2)$ dei fibrati vettoriali stabili di rango 2 su ${\mathbb{P}}^2$ e le loro risoluzioni libere minimali. Ne segue una dimostrazione piuttosto semplice dell'irriducibilità di ${\mathfrak{M}}_{{\mathbb{P}}^2}(2,c_1,c_2)$.

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