TY - THES
T1 - Biregular and Birational Geometry of Algebraic Varieties
Y1 - 2013
A1 - Alex Massarenti
KW - Moduli spaces of curves, automorphisms, Hassett's moduli spaces, varieties of sums of powers
AB - 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.
PB - SISSA
U1 - 6962
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -