UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 23, 2016

939 Evans Hall

3:45PM - 6:00PM: Moduli spaces of curves with nonspecial divisors and A-infinity algebras

Alexander Polishchuk

In the first hour I will give an introduction to A-infinity algebras and will explain how studying certain A-infinity algebras associated with curves one gets an isomorphism between a moduli space of A-infinity algebras and the moduli space of pointed curves (with possibly non-nodal singularities) such that the marked points form a nonspecial ample divisor. In the second hour I will discuss geometry of the latter moduli spaces. I will show that such curves have natural projective embeddings, with a canonical choice of homogenous coordinates up to rescaling. Using Groebner bases technique this leads to the identification of the moduli with the quotient of an affine scheme by the torus action. In the genus 1 case I will describe explicitly the corresponding GIT stability conditions. In characteristic zero this picture is complemented by canonical choices of formal parameters at marked points, leading to an interpretation of the moduli spaces in terms of the Krichever map.

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