A note on the existence of stable vector bundles on Enriques surfaces

Howard Nuer

doi:10.1007/s00029-015-0218-6

A note on the existence of stable vector bundles on Enriques surfaces

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the non-emptiness and irreducibility of M_H(v, L) , the moduli space of Gieseker semistable sheaves on an unnodal Enriques surface Y with primitive Mukai vector v of positive rank and determinant L with respect to a generic polarization H. This completes the chain of progress initiated by Kim (Nagoya Math J 150:85–94, 1998). We also show that the stable locus MHs(v)≠∅ for non-primitive v with v²> 0.

Original language	English
Pages (from-to)	1117-1156
Number of pages	40
Journal	Selecta Mathematica, New Series
Volume	22
Issue number	3
DOIs	https://doi.org/10.1007/s00029-015-0218-6
State	Published - 1 Jul 2016
Externally published	Yes

Keywords

Enriques surfaces
Mumford–Thaddeus principle
Stable vector bundles

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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10.1007/s00029-015-0218-6

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abstract = "We prove the non-emptiness and irreducibility of MH(v, L) , the moduli space of Gieseker semistable sheaves on an unnodal Enriques surface Y with primitive Mukai vector v of positive rank and determinant L with respect to a generic polarization H. This completes the chain of progress initiated by Kim (Nagoya Math J 150:85–94, 1998). We also show that the stable locus MHs(v)≠∅ for non-primitive v with v2> 0.",

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AB - We prove the non-emptiness and irreducibility of MH(v, L) , the moduli space of Gieseker semistable sheaves on an unnodal Enriques surface Y with primitive Mukai vector v of positive rank and determinant L with respect to a generic polarization H. This completes the chain of progress initiated by Kim (Nagoya Math J 150:85–94, 1998). We also show that the stable locus MHs(v)≠∅ for non-primitive v with v2> 0.

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KW - Mumford–Thaddeus principle

KW - Stable vector bundles

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A note on the existence of stable vector bundles on Enriques surfaces

Abstract

Keywords

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