Files in this item
Files | Description | Format |
---|---|---|
application/pdf ![]() | (no description provided) |
Description
Title: | Deformations of the Hilbert scheme of points on a del Pezzo surface |
Author(s): | Li, Chunyi |
Director of Research: | Nevins, Thomas A. |
Doctoral Committee Chair(s): | Katz, Sheldon |
Doctoral Committee Member(s): | Nevins, Thomas A.; Bradlow, Steven B.; Schenck, Henry K. |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Hilbert scheme
deformation theory del Pezzo surface |
Abstract: | The Hilbert scheme of $n$ points in a smooth del Pezzo surface $S$ parameterizes zero-dimensional subschemes with length $n$ on $S$. We construct a flat family of deformations of Hilb$^n S$ which can be conceptually understood as the family of Hilbert schemes of points on a family of noncommutative deformations of $S$. Further we show that each deformed Hilb$^n S$ carries a generically symplectic holomorphic Poisson structure. Moreover, the generic deformation of Hilb$^nS$ has a $(k+2)$-dimensional moduli space, where the del Pezzo surface is the blow up of projective plane at $k$ sufficiently general points; and each of the fibers is of the form that we construct. Our work generalizes results of Nevins-Stafford constructing deformations of the Hilbert scheme of points on the plane, and of Hitchin studying those deformations from the viewpoint of Poisson geometry. |
Issue Date: | 2014-05-30 |
URI: | http://hdl.handle.net/2142/49684 |
Rights Information: | Copyright 2014 Chunyi Li |
Date Available in IDEALS: | 2014-05-30 2016-09-22 |
Date Deposited: | 2014-05 |
This item appears in the following Collection(s)
-
Dissertations and Theses - Mathematics
-
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois