Deformations of zero-dimensional schemes and applications

Abstract

In this thesis we consider the geometry of the Hilbert scheme of points in P^n, concentrating on the locus of points corresponding to the Gorenstein subschemes of P^n. 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.

v2: some minor corrections made. 29 pages. This is an MSc thesis done on the University of Warsaw; my adviser is Jarosław Buczyński

References in corpus (2)

• Equations for secant varieties of Veronese and other varieties
• Local finite dimensional Gorenstein k-algebras having Hilbert function (1,5,5,1) are smoothable

Cited by in corpus (5)

• Irreducibility of the Gorenstein loci of Hilbert schemes via ray families
• Symmetric Decomposition of the Associated Graded Algebra of an Artinian Gorenstein Algebra
• More on the admissible condition on differentiable maps $\phi :(X^{Az},E;\nabla )\to Y$ in the construction of the non-Abelian Dirac-Born-Infeld action $S_{DBI}(\phi ,\nabla )$
• Finite schemes and secant varieties over arbitrary characteristic
• Non-reducedness of the Hilbert schemes of few points