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arXiv · 2003.02727

On the Segre Invariant for rank two vector bundles on \mathbb{P}^2

L. Roa-Leguizamón·H. Torres López·A. G. Zamora
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Abstract

We extend the concept of Segre's Invariant to vector bundles on a surface $X$. For $X=\mathbb{P}^2$ we determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle with given Chern's classes. The irreducibility of strata with fixed Segre's invariant is proved and its dimensions are computed. Finally, we present applications to the Brill-Noether's Theory for rank $2$ vector bundles on $\mathbb{P}^2.$

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L. Roa-Leguizamón, H. Torres López, A. G. Zamora. 2020-03-05. On the Segre Invariant for rank two vector bundles on \mathbb{P}^2. https://doi.org/10.1515/advgeom-2021-0003

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