|Date: Monday, October 29, 2018
Location: 4096 East Hall (4:00 PM to 6:00 PM)
Title: Virtual cycles via deformation and localization
Abstract: The moduli space of stable maps to the quintic is compact and carries a virtual fundamental class. It is naturally contained in Chang-Li's moduli space of stable maps with p-fields, a moduli space taking for input a base P^4 and line bundle O(5). This later moduli space is not compact (in fact, it is a cone over the moduli space of stable maps), but it carries a cosection localized virtual fundamental class defined by the quintic polynomial x_1^5+ . . . +x_5^5. Chang-Li show that the cosection localized virtual fundamental class is supported on the moduli space of stable maps, and is equal to the traditional virtual fundamental class living there.
I will present a work joint with Qile Chen and Felix Janda in which we extend Chang-Li's construction to a complete intersection in a smooth projective variety. The argument uses a deformation to the normal cone to reduce the problem to a special case, and then localization to compute that case.
Speaker: Rachel Webb