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 ChangLi's moduli space of stable maps with pfields, 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. ChangLi 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 ChangLi'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.
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Speaker: Rachel Webb
Institution: UM
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