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

Dionisi, Carla ; Maggesi, Marco

Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003), p. 151-160 / Harvested from Biblioteca Digitale Italiana di Matematica

Abstract

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.

Résumé

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 $\mathfrak{M}_{\mathbb{P}^{2}}(2, c_{1}, c_{2})$.

Détail

Publié le : 2003-02-01

MR 1955702 | Zbl 1150.14002

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