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Arithmetically Gorenstein sets of points on general surfaces in P3

thesis
posted on 2013-04-09, 00:00 authored by Megan Patnott
This dissertation examines two questions. In the first two chapters, we study the minimal free resolution of a general set of points on a surface of degree d in P3. Our main result for this problem, contained in Chapter 2, is to give the form of the minimal free resolution of a general set of points on a cubic surface that has at most finitely many double points. We use liaison techniques and count syzygies. In the third and fourth chapters, we study the arithmetically Gorenstein sets of points on a general surface in P3. Our main result is a complete list of the h-vectors of arithmetically Gorenstein sets of points on a general sextic surface in P3. We use a connection between such sets of points and rank two arithmetically Cohen-Macaulay vector bundles on the surface, as well as liaison techniques and Terracini's lemma.

History

Date Modified

2017-06-05

Defense Date

2013-04-08

Research Director(s)

Juan Migliore

Committee Members

Claudia Polini Nero Budur Sonja Mapes

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Language

  • English

Alternate Identifier

etd-04092013-094050

Publisher

University of Notre Dame

Program Name

  • Mathematics (MATH)

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