%0 Thesis
%D 2013
%T Biregular and Birational Geometry of Algebraic Varieties
%A Alex Massarenti
%K Moduli spaces of curves, automorphisms, Hassett's moduli spaces, varieties of sums of powers
%X 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.
%I SISSA
%G en
%1 6962
%2 Mathematics
%4 1
%# MAT/03 GEOMETRIA
%$ Submitted by Alex Massarenti (massaren@sissa.it) on 2013-06-25T07:25:44Z
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%0 Journal Article
%J Le Matematiche 66 (2011) 137-151
%D 2011
%T Covered by lines and Conic connected varieties
%A Simone Marchesi
%A Alex Massarenti
%A Saeed Tafazolian
%X We study some properties of an embedded variety covered by lines and give a\\r\\nnumerical criterion ensuring the existence of a singular conic through two of\\r\\nits general points. We show that our criterion is sharp. Conic-connected,\\r\\ncovered by lines, QEL, LQEL, prime Fano, defective, and dual defective\\r\\nvarieties are closely related. We study some relations between the above\\r\\nmentioned classes of objects using celebrated results by Ein and Zak.
%B Le Matematiche 66 (2011) 137-151
%I Universita\\\' di Catania, Dipartimento di Matematica e Informatica
%G en
%U http://hdl.handle.net/1963/5788
%1 5641
%2 Mathematics
%3 Mathematical Physics
%4 -1
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