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Ulrich bundles on abelian surfaces

Author: Arnaud Beauville
Journal: Proc. Amer. Math. Soc. 144 (2016), 4609-4611
MSC (2010): Primary 14J60; Secondary 13D02
Published electronically: April 20, 2016
MathSciNet review: 3544513
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Abstract: We prove that any abelian surface admits a rank $ 2$ Ulrich bundle.

References [Enhancements On Off] (What's this?)

  • [AFO] M. Aprodu, G. Farkas, A. Ortega, Minimal resolutions, Chow forms and Ulrich bundles on $ K3$ surfaces, preprint arXiv:1212.6248. J. Reine Angew. Math., to appear.
  • [CKM] Emre Coskun, Rajesh S. Kulkarni, and Yusuf Mustopa, On representations of Clifford algebras of ternary cubic forms, New trends in noncommutative algebra, Contemp. Math., vol. 562, Amer. Math. Soc., Providence, RI, 2012, pp. 91-99. MR 2905555,
  • [HUB] J. Herzog, B. Ulrich, and J. Backelin, Linear maximal Cohen-Macaulay modules over strict complete intersections, J. Pure Appl. Algebra 71 (1991), no. 2-3, 187-202. MR 1117634 (92g:13011),
  • [ES] David Eisenbud, Frank-Olaf Schreyer, and Jerzy Weyman, Resultants and Chow forms via exterior syzygies, J. Amer. Math. Soc. 16 (2003), no. 3, 537-579. MR 1969204 (2004j:14067),
  • [HL] Daniel Huybrechts and Manfred Lehn, The geometry of moduli spaces of sheaves, 2nd ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2010. MR 2665168 (2011e:14017)
  • [M] Shigeru Mukai, Symplectic structure of the moduli space of sheaves on an abelian or $ K3$ surface, Invent. Math. 77 (1984), no. 1, 101-116. MR 751133 (85j:14016),

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Additional Information

Arnaud Beauville
Affiliation: Laboratoire J.-A. Dieudonné, UMR 7351 du CNRS, Université de Nice, Parc Valrose, F-06108 Nice cedex 2, France

Received by editor(s): December 9, 2015
Received by editor(s) in revised form: January 11, 2016
Published electronically: April 20, 2016
Communicated by: Lev Borisov
Article copyright: © Copyright 2016 American Mathematical Society

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