Deformations of zero-dimensional schemes and applications

2013/07/30 by Jelisiejew, Joachim
#13D10 #13H10 #14C05 #14D06 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.8108

Abstract

In this thesis we consider the geometry of the Hilbert scheme of points in Pⁿ, concentrating on the locus of points corresponding to the Gorenstein subschemes of Pⁿ. New results are given, most importantly we provide tools for constructing flat families and analysis of finite Gorenstein algebras and expose their efficiency by proving smoothability of certain families of algebras. Much of the existing theory and folklore is reviewed, providing a micro-encyclopaedic reference.

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