Syzygies, finite length modules, and random curves
arXiv:1403.0581
Abstract
We apply the theory of Groebner bases to the computation of free resolutions over a polynomial ring, the defining equations of a canonically embedded curve, and the unirationality of the moduli space of curves of a fixed genus.
31 pages, This article consists of extended notes from lectures by the second author at the Joint Introductory Workshop: Cluster Algebras and Commutative Algebra at the Mathematical Science Research Institute (MSRI) in Berkeley, California, in Fall 2012