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Dual complexes of mapping spaces in low genus

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If you have a question about this talk, please contact Dhruv Ranganathan .

I will discuss joint work with Terry Song studying dual boundary complexes of moduli spaces of maps from smooth pointed curves of genus g to projective space, for g = 0 and g = 1. In genus zero, a normal crossings compactification is provided by the Kontsevich moduli space. In genus one, a normal crossings compactification was given by Vakil and Zinger, and later furnished with a modular interpretation by Ranganathan, Santos-Parker, and Wise. I will discuss the geometry of these compactifications and the combinatorics of the resulting dual complexes. In particular, in both cases the dual complex will be seen to be contractible.

This talk is part of the Algebraic Geometry Seminar series.

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