University of Illinois at Chicago
Browse

File(s) under embargo

6

month(s)

7

day(s)

until file(s) become available

Severi Varieties and Sharp Bounds of Castelnuovo-Mumford Regularities

thesis
posted on 2022-08-01, 00:00 authored by Shijie Shang
In the first part of the thesis, we give a new proof of Zak's classification theorem of Severi varieties based on Zak's analysis of smooth quadrics on Severi varieties and classification of aCM bundles on smooth quadrics. In the second part of the thesis, we show that a bound of the Castelnuovo-Mumford regularity of any power of the ideal sheaf of a smooth projective complex variety X in a projective space of dimension r is sharp exactly for complete intersections, provided the variety X is cut out scheme-theoretically by several hypersurfaces in the projective space of dimension r.

History

Advisor

Ein, Lawrence

Chair

Ein, Lawrence

Department

Mathematics, Statistics and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

  • Doctoral

Degree name

PhD, Doctor of Philosophy

Committee Member

Coskun, Izzet Niu, Wenbo Ross, Julius Tucker, Kevin

Submitted date

August 2022

Thesis type

application/pdf

Language

  • en

Usage metrics

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC