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Lines on Cubic Threefolds and Fourfo...

Brooke, Corey Tucker.

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Lines on Cubic Threefolds and Fourfolds Containing a Plane.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lines on Cubic Threefolds and Fourfolds Containing a Plane./
Author:	Brooke, Corey Tucker.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	88 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=30525899
ISBN:	9798379953409

Lines on Cubic Threefolds and Fourfolds Containing a Plane.
Brooke, Corey Tucker.

Lines on Cubic Threefolds and Fourfolds Containing a Plane. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 88 p.

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

Thesis (Ph.D.)--University of Oregon, 2023.

This thesis describes the Fano scheme F(Y ) of lines on a general cubic threefold Y containing a plane over a field k of characteristic different from 2. One irreducible component of F(Y ) is birational (over k) to a torsor T of an abelian surface, and we apply the geometry and arithmetic of this torsor to answer two questions. First, when is a cubic threefold containing a plane rational over k, and second, how can one describe the rational Lagrangian fibration from the Fano variety of lines on a cubic fourfold containing a plane? To answer the first question, we apply recently developed intermediate Jacobian torsor obstructions and show that the existence over k of certain classical rationality constructions completely determines whether the threefold is rational over k. The second question, motivated by hyperk{phono}{middot}ahler geometry, we answer by giving an elementary construction that works over a broad class of base fields where hyperk{phono}{middot}ahler tools are not available; moreover, we relate our construction to other descriptions of the rational Lagrangian fibration in the case k = C.{A0}

ISBN: 9798379953409Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Cubic threefolds

Lines on Cubic Threefolds and Fourfolds Containing a Plane.
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020 $a 9798379953409
035 $a (MiAaPQ)AAI30525899
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100 1 $a Brooke, Corey Tucker. $3 3771621
245 1 0 $a Lines on Cubic Threefolds and Fourfolds Containing a Plane.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 88 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
500 $a Advisor: Addington, Nicolas.
502 $a Thesis (Ph.D.)--University of Oregon, 2023.
520 $a This thesis describes the Fano scheme F(Y ) of lines on a general cubic threefold Y containing a plane over a field k of characteristic different from 2. One irreducible component of F(Y ) is birational (over k) to a torsor T of an abelian surface, and we apply the geometry and arithmetic of this torsor to answer two questions. First, when is a cubic threefold containing a plane rational over k, and second, how can one describe the rational Lagrangian fibration from the Fano variety of lines on a cubic fourfold containing a plane? To answer the first question, we apply recently developed intermediate Jacobian torsor obstructions and show that the existence over k of certain classical rationality constructions completely determines whether the threefold is rational over k. The second question, motivated by hyperk{phono}{middot}ahler geometry, we answer by giving an elementary construction that works over a broad class of base fields where hyperk{phono}{middot}ahler tools are not available; moreover, we relate our construction to other descriptions of the rational Lagrangian fibration in the case k = C.{A0}
590 $a School code: 0171.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Cubic threefolds
653 $a Lines
653 $a Plane
653 $a Elementary construction
653 $a Lagrangian fibration
690 $a 0405
690 $a 0642
710 2 $a University of Oregon. $b Department of Mathematics. $3 3173590
773 0 $t Dissertations Abstracts International $g 85-01B.
790 $a 0171
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30525899