In this paper we survey some results on the symmetric semi-perfect obstruction theory on a Deligne-Mumford stack X constructed by Chang-Li,and Behrend’s theorem equating the weighted Euler characteristic of X and the...In this paper we survey some results on the symmetric semi-perfect obstruction theory on a Deligne-Mumford stack X constructed by Chang-Li,and Behrend’s theorem equating the weighted Euler characteristic of X and the virtual count of X by symmetric semi-perfect obstruction theories.As an application,we prove that Joyce’s d-critical scheme admits a symmetric semi-perfect obstruction theory,which can be applied to the virtual Euler characteristics by Jiang-Thomas.展开更多
Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler charact...Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by a cyclic L∞-algebra L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that the Behrend function depends only on the formal neighborhood of the moduli space.展开更多
文摘In this paper we survey some results on the symmetric semi-perfect obstruction theory on a Deligne-Mumford stack X constructed by Chang-Li,and Behrend’s theorem equating the weighted Euler characteristic of X and the virtual count of X by symmetric semi-perfect obstruction theories.As an application,we prove that Joyce’s d-critical scheme admits a symmetric semi-perfect obstruction theory,which can be applied to the virtual Euler characteristics by Jiang-Thomas.
基金Supported by Simon Foundation Collaboration Grants(Grant No.311837)
文摘Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by a cyclic L∞-algebra L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that the Behrend function depends only on the formal neighborhood of the moduli space.
