UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

April 02, 2013

939 Evans Hall

3:45PM: Links and resolutions of rational and Cohen-Macaulay singularities

J'anos Koll'ar

We study the connection between algebraic properties of singularities and the topology of their links and their resolutions.

5:00PM: Tropicalization of classical moduli spaces

Qingchun Ren

The image of the complement of a hyperplane arrangement under a monomial map can be tropicalized combinatorially using matroid theory. We apply this to classical moduli spaces that are associated with complex reflection arrangements. Starting from modular curves, we visit the Segre cubic, the Igusa quartic, and moduli of marked del Pezzo surfaces of degrees 2 and 3. Our primary example is the Burkhardt quartic, whose tropicalization is a 3-dimensional fan in 39-dimensional space. This effectuates a synthesis of concrete and abstract approaches to tropical moduli of genus 2 curves. (Work with Steven Sam and Bernd Sturmfels)

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