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Biregular and Birational Geometry of Algebraic Varieties

TitleBiregular and Birational Geometry of Algebraic Varieties
Publication TypeThesis
Year of Publication2013
AuthorsMassarenti, A
KeywordsModuli spaces of curves, automorphisms, Hassett's moduli spaces, varieties of sums of powers

Every area of mathematics is characterized by a guiding problem. In algebraic geometry
such problem is the classification of algebraic varieties. In its strongest form it means to
classify varieties up to biregular morphisms. However, birationally equivalent varieties share many interesting properties. Therefore for any birational equivalence class it is natural to work out a variety, which is the simplest in a suitable sense, and then study these varieties. This is the aim of birational geometry. In the first part of this thesis we deal with the biregular geometry of moduli spaces of curves, and in particular with their biregular automorphisms. However, in doing this we will consider some aspects of their birational geometry. The second part is devoted to the birational geometry of varieties of sums of powers and to some related problems which will lead us to computational geometry and geometric complexity theory.

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Submitted by Alex Massarenti ( on 2013-06-25T07:25:44Z
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