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Licensed Unlicensed Requires Authentication Published by De Gruyter February 22, 2012

Semi-homogeneous sheaves, Fourier–Mukai transforms and moduli of stable sheaves on abelian surfaces

  • Shintarou Yanagida EMAIL logo and Kōta Yoshioka

Abstract.

This paper studies stable sheaves on abelian surfaces of Picard number one. Our main tools are semi-homogeneous sheaves and Fourier–Mukai transforms. We introduce the notion of semi-homogeneous presentation and investigate the behavior of stable sheaves under Fourier–Mukai transforms. As a consequence, an affirmative answer is given to the conjecture proposed by Mukai in the 1980s. This paper also includes an explicit description of the birational correspondence between the moduli spaces of stable sheaves and the Hilbert schemes.

Received: 2010-04-06
Revised: 2011-11-21
Published Online: 2012-02-22
Published in Print: 2013-11-01

© 2013 by Walter de Gruyter Berlin Boston

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