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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2013, Issue 684


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

Shintarou Yanagida / Kōta Yoshioka
Published Online: 2012-02-22 | DOI: https://doi.org/10.1515/crelle-2011-0010


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.

About the article

Received: 2010-04-06

Revised: 2011-11-21

Published Online: 2012-02-22

Published in Print: 2013-11-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2013, Issue 684, Pages 31–86, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2011-0010.

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Shintarou Yanagida and Kōta Yoshioka
Mathematische Zeitschrift, 2014, Volume 276, Number 1-2, Page 571

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