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OBSTRUCTED BUNDLES OF RANK TWO ON A QUINTIC SURFACE

NICOLE MESTRANO

CNRS, Laboratoire J. A. Dieudonné, UMR 6621, Université de Nice-Sophia Antipolis, 06108 Nice, Cedex 2, France

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and

CARLOS SIMPSON

CNRS, Laboratoire J. A. Dieudonné, UMR 6621, Université de Nice-Sophia Antipolis, 06108 Nice, Cedex 2, France

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https://doi.org/10.1142/S0129167X11007045Cited by:10 (Source: Crossref)

Abstract

In this note we consider the moduli space of stable bundles of rank two on a very general quintic surface. We study the potentially obstructed points of the moduli space via the spectral covering of a twisted endomorphism. This analysis leads to generically non-reduced components of the moduli space, and components which are generically smooth of more than the expected dimension. We obtain a sharp bound asked for by O'Grady on when the moduli space is good.

To the memory of Masaki Maruyama

Keywords:

AMSC: Primary 14D20, Secondary 14B05, Secondary 14J29

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