01444nas a2200121 4500008004100000245006100041210006100102260001000163520093500173653009701108100002101205856009601226 2013 en d00aBiregular and Birational Geometry of Algebraic Varieties0 aBiregular and Birational Geometry of Algebraic Varieties bSISSA3 aEvery 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.10aModuli spaces of curves, automorphisms, Hassett's moduli spaces, varieties of sums of powers1 aMassarenti, Alex uhttps://www.math.sissa.it/publication/biregular-and-birational-geometry-algebraic-varieties