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.
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@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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.1016/j.crma.2017.09.005/
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