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Divisor Varieties and Syzygies of Sy...

Sheridan, John Thomas.

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Divisor Varieties and Syzygies of Symmetric Products of Curves.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Divisor Varieties and Syzygies of Symmetric Products of Curves./
Author:	Sheridan, John Thomas.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	101 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
Contained By:	Dissertations Abstracts International82-05B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28090032
ISBN:	9798678199249

Divisor Varieties and Syzygies of Symmetric Products of Curves.
Sheridan, John Thomas.

Divisor Varieties and Syzygies of Symmetric Products of Curves. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 101 p.

Source: Dissertations Abstracts International, Volume: 82-05, Section: B.

Thesis (Ph.D.)--State University of New York at Stony Brook, 2020.

This item must not be sold to any third party vendors.

We take two themes in algebraic geometry which are well understood and indeed classical in the case of curves - Brill-Noether theory of a general curve, and the theory of syzygies of a high degree curve in projective space - and we study analogous questions in the less well understood setting of higher dimensional varieties. Specifically, we focus on those higher dimensional varieties which are symmetric products of a curve: in the first case, we describe the geometry of parameter spaces of effective divisors (``divisor varieties") associated to these symmetric products, indicating how the properties (new in the higher dimensional setting) of singularity and reducibility of these divisor varieties reflect the geometry of the underlying curve. In the second case we study how much syzygetic information about an embedded curve - that is, information about the equations defining the curve in its projective embedding - can be transferred to its symmetric product when the latter is embedded in projective space in a natural way using secant planes of the embedded curve.

ISBN: 9798678199249Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Algebraic geometry

Divisor Varieties and Syzygies of Symmetric Products of Curves.
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100 1 $a Sheridan, John Thomas. $3 3558928
245 1 0 $a Divisor Varieties and Syzygies of Symmetric Products of Curves.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 101 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
500 $a Advisor: Lazarsfeld, Robert.
502 $a Thesis (Ph.D.)--State University of New York at Stony Brook, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a We take two themes in algebraic geometry which are well understood and indeed classical in the case of curves - Brill-Noether theory of a general curve, and the theory of syzygies of a high degree curve in projective space - and we study analogous questions in the less well understood setting of higher dimensional varieties. Specifically, we focus on those higher dimensional varieties which are symmetric products of a curve: in the first case, we describe the geometry of parameter spaces of effective divisors (``divisor varieties") associated to these symmetric products, indicating how the properties (new in the higher dimensional setting) of singularity and reducibility of these divisor varieties reflect the geometry of the underlying curve. In the second case we study how much syzygetic information about an embedded curve - that is, information about the equations defining the curve in its projective embedding - can be transferred to its symmetric product when the latter is embedded in projective space in a natural way using secant planes of the embedded curve.
590 $a School code: 0771.
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical mathematics. $3 3173530
653 $a Algebraic geometry
653 $a Curve
653 $a Divisor
653 $a Symmetric product
690 $a 0405
690 $a 0364
690 $a 0642
710 2 $a State University of New York at Stony Brook. $b Mathematics. $3 2096807
773 0 $t Dissertations Abstracts International $g 82-05B.
790 $a 0771
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28090032