# Special Year Seminar II

## MM-curves

For an embedded stable curve over the real numbers we introduce a hyperplane arrangement in the tangent space of the Hilbert scheme. The connected components of its complement are labeled by embeddings of the graph of the stable curve to a compact surface. We explain how the real type of a deformation of the curve is determined by the topology of such a surface. Finally, we prove that a so-called graph curve is the special fiber of a maximal Mumford curve (MM-curve) if and only if the graph is planar.

This is based on a joint work with Bernd Sturmfels and Raluca Vlad.

## Date & Time

October 31, 2024 | 10:00am – 12:00pm

### Location

Simonyi 101 and Remote Access### Speakers

Mario Kummer, Technische Universität Dresden

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## Notes

Video link: https://www.ias.edu/video/mm-curves