On some moduli spaces of bundles on surfaces, II

Author:
C. G. Madonna

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3397-3408

MSC (2010):
Primary 14D20, 14J28

DOI:
https://doi.org/10.1090/S0002-9939-2012-11251-1

Published electronically:
February 23, 2012

MathSciNet review:
2929009

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give several examples of the existence of infinitely many divisorial conditions on the moduli space of polarized surfaces of degree , , and Picard number , such that for a general surface satisfying these conditions the moduli space of sheaves is birationally equivalent to the Hilbert scheme of zero-dimensional subschemes of of length equal to . This result generalizes a result of Nikulin when and an earlier result of the author when , .

**1.**A. Beauville,*Variétés Kähleriennes dont la première classe de Chern est nulle*, J. Differential Geom.**18**(1983), no. 4, 755-782. MR**730926 (86c:32030)****2.**C.G. Madonna,*On some moduli spaces of bundles on surfaces*, Monatsh. Math.**146**(2005), 333-339. MR**2191732 (2006j:14061)****3.**C. Madonna and V.V. Nikulin,*On a classical correspondence between surfaces*, Proc. Steklov Inst. of Math.**241**(2003), 120-153. MR**2024049 (2004m:14080)****4.**C.G. Madonna and V.V. Nikulin,*Explicit correspondences of a surface with itself*, Izv. Math.**72**(2008), no. 3, 497-508. MR**2432754 (2009e:14061)****5.**Sh. Mukai,*On the moduli space of bundles on surfaces I*, in: Vector bundles on algebraic varieties, Tata Inst. Fund. Res. Studies in Math.**11**(1987), 341-413. MR**893604 (88i:14036)****6.**Sh. Mukai,*Moduli of vector bundles on surfaces and symplectic manifolds*, Sugaku Expositions**1**(1988), no. 2, 139-174. MR**922020 (89h:32057)****7.**V.V. Nikulin,*Integral symmetric bilinear forms and some of their geometric applications*, Math USSR-Izv.**14**(1980), no. 1, 103-167. MR**525944 (80j:10031)****8.**V.V. Nikulin,*On correspondences of a surface with itself. I*, Proc. Steklov Inst. of Math.**246**(2004), 204-226. MR**2101295 (2005j:14055)****9.**V.V. Nikulin,*On correspondences of a surface with itself. II*, Contemporary Mathematics**422**, Amer. Math. Soc., Providence, RI, 2007, 121-172. MR**2296436 (2008b:14061)****10.**V.V. Nikulin,*Self-correspondences of a surface via moduli of sheaves*, in: Y. Tschinkel and Y. Zarhin (eds.), Algebra, Arithmetic, and Geometry. Volume II: In Honor of Yu. I. Manin, 2009, Birkhäuser Boston, 439-464. MR**2641198 (2011g:14032)****11.**A.N. Tyurin,*Cycles, curves and vector bundles on algebraic surfaces*, Duke Math. J.**54**(1987), no. 1, 1-26. MR**885772 (88m:14004)****12.**K.Yoshioka,*Some examples of Mukai's reflections on surfaces*, J. Reine Angew. Math.**515**(1999), 97-123. MR**1717621 (2000h:14028)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2010):
14D20,
14J28

Retrieve articles in all journals with MSC (2010): 14D20, 14J28

Additional Information

**C. G. Madonna**

Affiliation:
Faculty of Teacher Training and Education, Autonoma University of Madrid, Campus de Cantoblanco, C/Fco. Tomas y Valiente 3, Madrid E-28049, Spain

Email:
carlo.madonna@uam.es

DOI:
https://doi.org/10.1090/S0002-9939-2012-11251-1

Received by editor(s):
August 17, 2010

Received by editor(s) in revised form:
April 12, 2011

Published electronically:
February 23, 2012

Additional Notes:
The author was supported by EPSRC grant EP/D061997/1. The author is a member of project MTM2007-67623, founded by the Spanish MEC

Communicated by:
Lev Borisov

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.