Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Ulrich bundles on Veronese surfaces


Authors: Emre Coskun and Ozhan Genc
Journal: Proc. Amer. Math. Soc. 145 (2017), 4687-4701
MSC (2010): Primary 14J60
DOI: https://doi.org/10.1090/proc/13659
Published electronically: May 30, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every Ulrich bundle on the Veronese surface has a resolution in terms of twists of the trivial bundle over $ \mathbb{P}^{2}$. Using this classification, we prove existence results for stable Ulrich bundles over $ \mathbb{P}^{k}$ with respect to an arbitrary polarization $ dH$.


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

  • [1] Constantin Bănică, Smooth reflexive sheaves, Proceedings of the Colloquium on Complex Analysis and the Sixth Romanian-Finnish Seminar, 1991, pp. 571-593. MR 1172165
  • [2] Arnaud Beauville, Determinantal hypersurfaces, Michigan Math. J. 48 (2000), 39-64. Dedicated to William Fulton on the occasion of his 60th birthday. MR 1786479 (2002b:14060), https://doi.org/10.1307/mmj/1030132707
  • [3] Marta Casanellas, Robin Hartshorne, Florian Geiss, and Frank-Olaf Schreyer, Stable Ulrich bundles, Internat. J. Math. 23 (2012), no. 8, 1250083, 50. MR 2949221, https://doi.org/10.1142/S0129167X12500838
  • [4] 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, https://doi.org/10.1090/conm/562/11132
  • [5] Emre Coskun, Rajesh S. Kulkarni, and Yusuf Mustopa, The geometry of Ulrich bundles on del Pezzo surfaces, J. Algebra 375 (2013), 280-301. MR 2998957, https://doi.org/10.1016/j.jalgebra.2012.08.032
  • [6] 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, https://doi.org/10.1090/S0894-0347-03-00423-5
  • [7] David Eisenbud and Frank-Olaf Schreyer, Boij-Söderberg theory, Combinatorial aspects of commutative algebra and algebraic geometry, Abel Symp., vol. 6, Springer, Berlin, 2011, pp. 35-48. MR 2810424, https://doi.org/10.1007/978-3-642-19492-4_3
  • [8] Gavril Farkas, Mircea Mustaţa, and Mihnea Popa, Divisors on $ {\scr M}_{g,g+1}$ and the minimal resolution conjecture for points on canonical curves, Ann. Sci. École Norm. Sup. (4) 36 (2003), no. 4, 553-581 (English, with English and French summaries). MR 2013926 (2005b:14051), https://doi.org/10.1016/S0012-9593(03)00022-3
  • [9] William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620
  • [10] Daniel Huybrechts and Manfred Lehn, The geometry of moduli spaces of sheaves, 2nd ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2010. MR 2665168
  • [11] Anna Lorenzini, The minimal resolution conjecture, J. Algebra 156 (1993), no. 1, 5-35. MR 1213782 (94g:13005), https://doi.org/10.1006/jabr.1993.1060
  • [12] Christian Okonek, Michael Schneider, and Heinz Spindler, Vector bundles on complex projective spaces, Modern Birkhäuser Classics, Birkhäuser/Springer Basel AG, Basel, 2011. Corrected reprint of the 1988 edition; With an appendix by S. I. Gelfand. MR 2815674

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14J60

Retrieve articles in all journals with MSC (2010): 14J60


Additional Information

Emre Coskun
Affiliation: Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey
Email: emcoskun@metu.edu.tr

Ozhan Genc
Affiliation: Mathematics Research and Teaching Group, Middle East Technical University, 06800, Ankara, Turkey
Address at time of publication: Mathematics Research and Teaching Group, Middle East Technical University, Northern Cyprus Campus, KKTC, Mersin 10, Turkey
Email: ozhangenc@gmail.com

DOI: https://doi.org/10.1090/proc/13659
Received by editor(s): September 22, 2016
Received by editor(s) in revised form: December 6, 2016
Published electronically: May 30, 2017
Additional Notes: The first author was supported by TUBITAK project 114F116.
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society