Filippo Viviani

Gilberto Bini

Fabio Felici

Margarida Melo

We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5a

Geometric Invariant Theory for Polarized Curves

Aldo Conca

Sandra Di Rocco

Jan Draisma

June Huh

Bernd Sturmfels

Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions and enumerative geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed with a rich combinatorial structure. Relevant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications.

Levico Terme, Italy 2013, Editors: Sandra Di Rocco, Bernd Sturmfels

Combinatorial Algebraic Geometry

Filippo Viviani

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