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Student
Title
Supervisor
Faculty
Educational Programme
Final Grade
Year of Graduation
Pavel Kovalev
Families of Algebraic Curves and of Their Mappings
Mathematics
(Bachelor’s programme)
2017
In this work, we study spaces of holomorphic degree n mappings from algebraic curves to algebraic curves with a marked point whose inverse image consists of n numbered simple points. We review a description of the corresponding space of mappings to curves of genus zero as an open dense subset of the total space of a certain vector bundle over the moduli space M_{0;n}. Further, we make first steps towards constructing a similar description of the space of mappings to elliptic curves, i.e., curves of genus one. Along the way, we introduce the basic notions that are of interest to us in both formal and informal manner.

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