Curves, maps, and singularities in genus one

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• Dhruv Ranganathan (MIT/Cambridge)
• Wednesday 10 October 2018, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Mark Gross.

I will outline a new framework based on tropical geometry to study genus one curve singularities and discuss its relationship with the geometry of moduli spaces. I will focus on the application of this framework to construct new nonsingular compact moduli spaces parameterizing elliptic curves in projective space. This also reveals a modular interpretation for Vakil and Zinger’s famously difficult desingularization of the space of elliptic curves in projective space, as well as a short and conceptual proof of that result. The framework also gives rise to new insights into the Hassett—Keel program for spaces of elliptic curves. This is based on joint work with Keli Santos-Parker and Jonathan Wise.

This talk is part of the Algebraic Geometry Seminar series.

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