UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 18, 2020

939 Evans Hall

3:45PM: Derived invariants of varieties in positive characteristic

Daniel Bragg

A fundamental derived invariant associated to a smooth projective variety is its Hochschild homology. In positive characteristic, topological Hochschild homology gives another canonical derived invariant. We will explain how to compute with this object in practice, and as a consequence obtain some new restrictions on the Hodge numbers of derived equivalent varieties in positive characteristic. We will also present an example of two derived equivalent 3-folds in characteristic 3 with different Hodge numbers (found using Macaulay2). This is joint work with Benjamin Antieau and Nick Addington.

5:00PM: Geometry of Ellipses

Yuhan Jiang

A k-ellipse is a plane curve consisting of all points whose distances from k fixed foci sum to a constant. This talk concerns the singularities and genus of the Zariski closure of k-ellipses in the complex projective plane. At the end, we will discuss the canonical images of 3-ellipses in the moduli space of genus 3 curves.

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