Author:
Occhetta Gianluca,Romano Eleonora A.,Solá Conde Luis E.,Wiśniewski Jarosław A.
Abstract
AbstractWe link small modifications of projective varieties with a $${\mathbb {C}}^*$$
C
∗
-action to their GIT quotients. Namely, using flips with centers in closures of Białynicki-Birula cells, we produce a system of birational equivariant modifications of the original variety, which includes those on which a quotient map extends from a set of semistable points to a regular morphism. The structure of the modifications is completely described for the blowup along the sink and the source of smooth varieties with Picard number one with a $${\mathbb {C}}^*$$
C
∗
-action which has no finite isotropy for any point. Examples can be constructed upon homogeneous varieties with a $${\mathbb {C}}^*$$
C
∗
-action associated to short grading of their Lie algebras.
Publisher
Springer Science and Business Media LLC
Reference29 articles.
1. Abramovich, D., Karu, K., Matsuki, K., Włodarczyk, J.: Torification and factorization of birational maps. J. Amer. Math. Soc. 15(3), 531–572 (2002)
2. Arzhantsev, I., Derenthal, U., Hausen, J., Laface, A.: Cox Rings. Cambridge Studies in Advanced Mathematics, vol. 144. Cambridge University Press, Cambridge (2015)
3. Beltrametti, M.C., Sommese, A.J.: The Adjunction Theory of Complex Projective Varieties. De Gruyter Expositions in Mathematics, vol. 16. de Gruyter, Berlin (1995)
4. Białynicki-Birula, A.: Some theorems on actions of algebraic groups. Ann. Math. 98, 480–497 (1973)
5. Białynicki-Birula, A., Carrell, J.B., McGovern, W.M.: Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action. Encyclopaedia of Mathematical Sciences, vol. 131. Springer, Berlin (2002)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献