Hyperelliptic limits of quadrics through canonical curves and the super-Schottky locus

Abstract: I will describe joint works with Eric Rains and with Giovanni Felder and David Kazhdan. The first part will be about a classical topic of quadrics through canonically embedded curves. We study limiting quadrics as canonical curves approach a hyperelliptic limit. There is a surprizingly simple description of all such limits. I will also discuss the connection to ribbon curves (which are thickenings of rational normal curves) and to the blow up of the moduli space of curves at the hyperelliptic locus. In the second part I will talk about the super-period map for supercurves and the calculation of its infinitesimal variation. This variation is given by a natural Massey product that can be defined for any curve with a theta-characteristic. Combining this with the result of part 1 we get some information about the super-Schottky locus.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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