On the Segre invariant for rank two vector bundles on ℙ2-Reference-Cited by-同舟云学术

On the Segre invariant for rank two vector bundles on ℙ2

Published:2021-07-07 Issue:4 Volume:21 Page:565-576
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Roa-Leguizamón L.¹,Torres-López H.²,Zamora A. G.³

Affiliation:

1. Instituto de Física y Matemáticas , Universidad Michoacana de San Nicolás de Hidalgo , Edificio C3, Ciudad Universitaria, C.P.58040 Morelia , Mich , México

2. CONACyT - U. A. Matemáticas, U. Autónoma de Zacatecas , Calzada Solidaridad entronque Paseo a la Bufa , C.P. 98000, Zacatecas , Zac , México

3. U. A. Matemáticas, U. Autónoma de Zacatecas , Calzada Solidaridad entronque Paseo a la Bufa , C.P. 98000, Zacatecas , Zac , México

Abstract

Abstract We extend the concept of the Segre invariant to vector bundles on a surface X. For X = ℙ2 we determine what numbers can appear as the Segre invariant of a rank 2 vector bundle with given Chern classes. The irreducibility of strata with fixed Segre invariant is proved and their dimensions are computed. Finally, we present applications to the Brill–Noether Theory for rank 2 vector bundles on ℙ2.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2021-0003/pdf

Reference18 articles.

1. W. P. Barth, K. Hulek, C. A. M. Peters, A. Van de Ven, Compact complex surfaces. Springer 2004. MR2030225 Zbl 1036.14016

2. L. Brambila-Paz, H. Lange, A stratification of the moduli space of vector bundles on curves. J. Reine Angew. Math. 494 (1998), 173–187. MR1604403 Zbl 0919.14016

3. I. Coskun, J. Huizenga, Weak Brill–Noether for rational surfaces. In: Local and global methods in algebraic geometry, volume 712 of Contemp. Math., 81–104, Amer. Math. Soc. 2018. MR3832400 Zbl 1401.14186

4. L. Costa, R. M. Miró-Roig, Brill–Noether theory for moduli spaces of sheaves on algebraic varieties. Forum Math. 22 (2010), 411–432. MR2652705 Zbl 1190.14040

5. R. Friedman, Algebraic surfaces and holomorphic vector bundles. Springer 1998. MR1600388 Zbl 0902.14029

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