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On Complete Subvarieties of the Moduli Spaces of Curves

Student: Denisova Elena

Supervisor: Alexei Gorinov

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2019

We prove that a curve in the space of non-singular curves of degree d in CP2 gives a curve in the moduli space of smooth curves of the genus g = (d-1) (d-2) / 2 if and only if all local monodromies have finite order. This theorem can help in constructing an explicit example of a compact curve in the moduli space M3.

Full text (added May 31, 2019)

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