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Cubic Fourfolds and the Kuga-Satake ...

Annunziata, Michael.

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Cubic Fourfolds and the Kuga-Satake Construction.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Cubic Fourfolds and the Kuga-Satake Construction./
Author:	Annunziata, Michael.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	95 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: A.
Contained By:	Dissertations Abstracts International85-02A.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30632307
ISBN:	9798380106269

Cubic Fourfolds and the Kuga-Satake Construction.
Annunziata, Michael.

Cubic Fourfolds and the Kuga-Satake Construction. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 95 p.

Source: Dissertations Abstracts International, Volume: 85-02, Section: A.

Thesis (Ph.D.)--Michigan State University, 2023.

Given a \uD835\uDC3E3 surface \uD835\uDC46, the Kuga-Satake construction associates to \uD835\uDC46 an abelian variety \uD835\uDC3E\uD835\uDC46(\uD835\uDC46) known as the Kuga-Satake variety. Many similarities between cubic fourfolds \uD835\uDC4B and \uD835\uDC3E3 surfaces \uD835\uDC46 have been studied, particularly via Hodge theory by Hassett and derived categories by Kuznetsov. We study how the Kuga-Satake construction fits into this theory by studying the Kuga-Satake varieties of cubic fourfolds and their associated \uD835\uDC3E3 surfaces, endormorphism algebras of cubic fourfolds, and the derived category \uD835\uDC37\uD835\uDC4F (\uD835\uDC3E\uD835\uDC46(\uD835\uDC46)).

ISBN: 9798380106269Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Cubic fourfolds

Cubic Fourfolds and the Kuga-Satake Construction.
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035 $a (MiAaPQ)AAI30632307
035 $a AAI30632307
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040 $a MiAaPQ $c MiAaPQ
100 1 $a Annunziata, Michael. $3 3771633
245 1 0 $a Cubic Fourfolds and the Kuga-Satake Construction.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 95 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-02, Section: A.
500 $a Advisor: Kulkarni, Rajesh.
502 $a Thesis (Ph.D.)--Michigan State University, 2023.
520 $a Given a \uD835\uDC3E3 surface \uD835\uDC46, the Kuga-Satake construction associates to \uD835\uDC46 an abelian variety \uD835\uDC3E\uD835\uDC46(\uD835\uDC46) known as the Kuga-Satake variety. Many similarities between cubic fourfolds \uD835\uDC4B and \uD835\uDC3E3 surfaces \uD835\uDC46 have been studied, particularly via Hodge theory by Hassett and derived categories by Kuznetsov. We study how the Kuga-Satake construction fits into this theory by studying the Kuga-Satake varieties of cubic fourfolds and their associated \uD835\uDC3E3 surfaces, endormorphism algebras of cubic fourfolds, and the derived category \uD835\uDC37\uD835\uDC4F (\uD835\uDC3E\uD835\uDC46(\uD835\uDC46)).
590 $a School code: 0128.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Mathematics education. $3 641129
653 $a Cubic fourfolds
653 $a Kuga-Satake construction
653 $a Abelian variety
653 $a Hodge theory
653 $a \uD835\uDC3E3 surfaces
690 $a 0405
690 $a 0642
690 $a 0280
710 2 $a Michigan State University. $b Mathematics - Doctor of Philosophy. $3 3187827
773 0 $t Dissertations Abstracts International $g 85-02A.
790 $a 0128
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30632307