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Birational Geometry of Blowups of To...

Williamson, Noble.

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Birational Geometry of Blowups of Toric Projective Varieties.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Birational Geometry of Blowups of Toric Projective Varieties./
Author:	Williamson, Noble.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	66 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
Contained By:	Dissertations Abstracts International85-01B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30524553
ISBN:	9798379957346

Birational Geometry of Blowups of Toric Projective Varieties.
Williamson, Noble.

Birational Geometry of Blowups of Toric Projective Varieties. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 66 p.

Source: Dissertations Abstracts International, Volume: 85-01, Section: B.

Thesis (Ph.D.)--University of California, Riverside, 2023.

The Cox ring of an algebraic variety encodes important information on the birational geometry of the variety. When its Cox ring is finitely generated, a variety admits particularly desirable properties in the context of the Minimal Model Program and is called a Mori dream space. For example, all toric varieties are known to be Mori dream spaces so a natural next step in the problem is to study the birational geometry of projective varieties that can be constructed as blowups of toric varieties by studying their pseudoeffective cones and Cox rings. In this dissertation, we present a concrete criterion for the finite generation of the Cox ring of toric projective surfaces of Picard number one blown up at a smooth point using the coordinates of a polytope of the toric variety. We also present a criterion for the irreducibility of an effective divisor of the moduli space of n-pointed stable rational curves.

ISBN: 9798379957346Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Birational geometry

Birational Geometry of Blowups of Toric Projective Varieties.
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245 1 0 $a Birational Geometry of Blowups of Toric Projective Varieties.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 66 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
500 $a Advisor: Gonzalez, Jose.
502 $a Thesis (Ph.D.)--University of California, Riverside, 2023.
520 $a The Cox ring of an algebraic variety encodes important information on the birational geometry of the variety. When its Cox ring is finitely generated, a variety admits particularly desirable properties in the context of the Minimal Model Program and is called a Mori dream space. For example, all toric varieties are known to be Mori dream spaces so a natural next step in the problem is to study the birational geometry of projective varieties that can be constructed as blowups of toric varieties by studying their pseudoeffective cones and Cox rings. In this dissertation, we present a concrete criterion for the finite generation of the Cox ring of toric projective surfaces of Picard number one blown up at a smooth point using the coordinates of a polytope of the toric variety. We also present a criterion for the irreducibility of an effective divisor of the moduli space of n-pointed stable rational curves.
590 $a School code: 0032.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Birational geometry
653 $a Divisors
653 $a Cox ring
653 $a Pseudoeffective cones
653 $a Toric varieties
690 $a 0405
690 $a 0642
710 2 $a University of California, Riverside. $b Mathematics. $3 2101069
773 0 $t Dissertations Abstracts International $g 85-01B.
790 $a 0032
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30524553