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Birational Geometry of Genus One Fib...

Zanardini, Aline.

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Birational Geometry of Genus One Fibrations and Stability of Pencils of Plane Curves.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Birational Geometry of Genus One Fibrations and Stability of Pencils of Plane Curves./
Author:	Zanardini, Aline.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	233 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-11, Section: B.
Contained By:	Dissertations Abstracts International82-11B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28417381
ISBN:	9798738617645

Birational Geometry of Genus One Fibrations and Stability of Pencils of Plane Curves.
Zanardini, Aline.

Birational Geometry of Genus One Fibrations and Stability of Pencils of Plane Curves. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 233 p.

Source: Dissertations Abstracts International, Volume: 82-11, Section: B.

Thesis (Ph.D.)--University of Pennsylvania, 2021.

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

In the first part of this thesis we give a complete classification of relative log canonical models for genus one fibrations in dimensions two and three. More concretely, we generalize the work in [2] by considering both (i) the case where it is not assumed the existence of a section, but of a multisection instead; and (ii) the case of threefolds in one dimension higher. In the second part, we investigate the stability of pencils of plane curves in the sense of geometric invariant theory. One of our main results relates the stability of a pencil of plane curves P to the log canonical threshold of pairs (P.

ISBN: 9798738617645Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Genus one fibrations

Birational Geometry of Genus One Fibrations and Stability of Pencils of Plane Curves.
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100 1 $a Zanardini, Aline. $3 3558988
245 1 0 $a Birational Geometry of Genus One Fibrations and Stability of Pencils of Plane Curves.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 233 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-11, Section: B.
500 $a Advisor: Grassi, Antonella.
502 $a Thesis (Ph.D.)--University of Pennsylvania, 2021.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be sold to any third party vendors.
520 $a In the first part of this thesis we give a complete classification of relative log canonical models for genus one fibrations in dimensions two and three. More concretely, we generalize the work in [2] by considering both (i) the case where it is not assumed the existence of a section, but of a multisection instead; and (ii) the case of threefolds in one dimension higher. In the second part, we investigate the stability of pencils of plane curves in the sense of geometric invariant theory. One of our main results relates the stability of a pencil of plane curves P to the log canonical threshold of pairs (P.
520 $a 2,C_d), where C_d is a curve in P, thus extending an idea of Hacking [23] and Kim-Lee [27]. Part of our approach consists in observing that we can sometimes determine whether a pencil P is (semi)stable or not by looking at the stability of the curves lying on it. As a beautiful application, we completely describe the stability of Halphen pencils of index two -- classical geometric objects first introduced by Halphen in 1882 [24]. Inspired by the work of Miranda in [40], we provide explicit stability criteria in terms of the geometry of their associated rational elliptic surfaces.
590 $a School code: 0175.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Genus one fibrations
653 $a GIT stability
653 $a Halphen pencils
653 $a Log canonical threshold
653 $a Pencils of plane curves
653 $a Relative log canonical models
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a University of Pennsylvania. $b Mathematics. $3 2101086
773 0 $t Dissertations Abstracts International $g 82-11B.
790 $a 0175
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28417381