[Géométrie birationnelle de l'espace moduli des faisceaux purs sur une surface quadrique]
Dans cette note, nous étudions la géométrie birationnelle de l'espace des modules des faisceaux stables sur une quadrique, de polynôme de Hilbert et de classes de Chern . Pour cela, nous donnons une application birationnelle entre l'espace des modules et un fibré projectif au dessus d'une grassmanienne, qui est une composition d'éclatements et de contractions lisses.
We study birational geometry of the moduli space of stable sheaves on a quadric surface with Hilbert polynomial and . We describe a birational map between the moduli space and a projective bundle over a Grassmannian as a composition of smooth blow-ups/downs.
Accepté le :
Publié le :
@article{CRMATH_2017__355_10_1082_0,
author = {Chung, Kiryong and Moon, Han-Bom},
title = {Birational geometry of the moduli space of pure sheaves on quadric surface},
journal = {Comptes Rendus. Math\'ematique},
pages = {1082--1088},
publisher = {Elsevier},
volume = {355},
number = {10},
year = {2017},
doi = {10.1016/j.crma.2017.09.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.09.005/}
}
TY - JOUR AU - Chung, Kiryong AU - Moon, Han-Bom TI - Birational geometry of the moduli space of pure sheaves on quadric surface JO - Comptes Rendus. Mathématique PY - 2017 SP - 1082 EP - 1088 VL - 355 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.09.005/ DO - 10.1016/j.crma.2017.09.005 LA - en ID - CRMATH_2017__355_10_1082_0 ER -
%0 Journal Article %A Chung, Kiryong %A Moon, Han-Bom %T Birational geometry of the moduli space of pure sheaves on quadric surface %J Comptes Rendus. Mathématique %D 2017 %P 1082-1088 %V 355 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.09.005/ %R 10.1016/j.crma.2017.09.005 %G en %F CRMATH_2017__355_10_1082_0
Chung, Kiryong; Moon, Han-Bom. Birational geometry of the moduli space of pure sheaves on quadric surface. Comptes Rendus. Mathématique, Tome 355 (2017) no. 10, pp. 1082-1088. doi : 10.1016/j.crma.2017.09.005. http://www.numdam.org/articles/10.1016/j.crma.2017.09.005/
[1] The birational geometry of the Hilbert scheme of points on surfaces, Birational Geometry, Rational Curves, and Arithmetic, Springer, New York, 2013, pp. 15-55
[2] Enumerative Invariants for Local Calabi–Yau Threefolds, University of Illinois, Champaign, IL, USA, 2012 (Ph.D. Thesis)
[3] Moduli spaces of α-stable pairs and wall-crossing on , J. Math. Soc. Jpn., Volume 68 (2016) no. 2, pp. 685-789
[4] Moduli of sheaves supported on quartic space curves, Mich. Math. J., Volume 65 (2016) no. 3, pp. 637-671
[5] Chow ring of the moduli space of stable sheaves supported on quartic curves, Q. J. Math., Volume 68 (Sep. 2017) no. 3, pp. 851-887
[6] Supplement to “On the inverse of monoidal transformation”, Publ. Res. Inst. Math. Sci., Volume 7 (1971–1972), pp. 637-644
[7] Espaces de modules de systèmes cohérents, Int. J. Math., Volume 9 (1998) no. 5, pp. 545-598
[8] The Geometry of Moduli Spaces of Sheaves, Cambridge Math. Lib., Cambridge University Press, Cambridge, UK, 2010
[9] Moduli of representations of finite-dimensional algebras, Q. J. Math. Oxford Ser. (2), Volume 45 (1994) no. 180, pp. 515-530
[10] Birational Geometry of Algebraic Varieties, Camb. Tracts Math., vol. 134, Cambridge University Press, Cambridge, 1998
[11] Faisceaux semi-stables de dimension 1 sur le plan projectif, Rev. Roum. Math. Pures Appl., Volume 38 (1993) no. 7–8, pp. 635-678
[12] Systèmes cohérents et structures de niveau, Astérisque (1993) no. 214, p. 143
[13] Moduli of sheaves supported on curves of genus two in a quadric surface, 2016 | arXiv
[14] On a family of algebraic vector bundles, Number Theory, Algebraic Geometry, and Commutative Algebra, in Honor of Yasuo Akizuki, Kinokuniya, Tokyo, 1973, pp. 95-149
Cité par Sources :
