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Equivalence Between Kuznetsov Compon...

Chen, Qingjing.

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Equivalence Between Kuznetsov Components of Cubic Fourfolds and Gushel-Mukai Fourfolds.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Equivalence Between Kuznetsov Components of Cubic Fourfolds and Gushel-Mukai Fourfolds./
Author:	Chen, Qingjing.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	95 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
Contained By:	Dissertations Abstracts International85-02B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30530124
ISBN:	9798380158961

Equivalence Between Kuznetsov Components of Cubic Fourfolds and Gushel-Mukai Fourfolds.
Chen, Qingjing.

Equivalence Between Kuznetsov Components of Cubic Fourfolds and Gushel-Mukai Fourfolds. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 95 p.

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

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

There are two ways that certain Fano fourfolds (for example, cubic fourfolds and Gushel-Mukai fourfolds) can be associated with K3 surfaces. On the one hand, we can associate a K3 surface to the fourfold Hodge-theoretically, meaning the middle cohomology of the fourfold contains the middle cohomology of the K3 as a sub-Hodge structure; on the other hand, we can homologically associate a K3 to the fourfold, which is to require the Kuznetsov component of the fourfolds to be equivalent to the bounded derived of the K3. Conjecturally, one expect such K3 associations detect rationality of the fourfolds. It has been proved that for cubic fourfolds, these two types of K3 associations are equivalent, whereas for Gushel-Mukai fourfolds, Hodge-association of a K3 strictly implies homological association of a K3. We continue this line of study, instead of comparing fourfoldsK3 association we consider fourfolds-fourfolds association. We prove that, at least for a generic Gushel-Mukai fourfold in the Hodge-special loci, if it admits Hodgeassociated cubic fourfolds, then it admits a homological-associated one, and vice versa.

ISBN: 9798380158961Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Algebraic geometry

Equivalence Between Kuznetsov Components of Cubic Fourfolds and Gushel-Mukai Fourfolds.
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100 1 $a Chen, Qingjing. $3 3771623
245 1 0 $a Equivalence Between Kuznetsov Components of Cubic Fourfolds and Gushel-Mukai Fourfolds.
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: B.
500 $a Advisor: Zhao, Xiaolei.
502 $a Thesis (Ph.D.)--University of California, Santa Barbara, 2023.
520 $a There are two ways that certain Fano fourfolds (for example, cubic fourfolds and Gushel-Mukai fourfolds) can be associated with K3 surfaces. On the one hand, we can associate a K3 surface to the fourfold Hodge-theoretically, meaning the middle cohomology of the fourfold contains the middle cohomology of the K3 as a sub-Hodge structure; on the other hand, we can homologically associate a K3 to the fourfold, which is to require the Kuznetsov component of the fourfolds to be equivalent to the bounded derived of the K3. Conjecturally, one expect such K3 associations detect rationality of the fourfolds. It has been proved that for cubic fourfolds, these two types of K3 associations are equivalent, whereas for Gushel-Mukai fourfolds, Hodge-association of a K3 strictly implies homological association of a K3. We continue this line of study, instead of comparing fourfoldsK3 association we consider fourfolds-fourfolds association. We prove that, at least for a generic Gushel-Mukai fourfold in the Hodge-special loci, if it admits Hodgeassociated cubic fourfolds, then it admits a homological-associated one, and vice versa.
590 $a School code: 0035.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Algebraic geometry
653 $a Deformation theory
653 $a Cubic fourfolds
653 $a Hodge theory
653 $a Kuznetsov components
653 $a Gushel-Mukai fourfolds
690 $a 0405
690 $a 0642
710 2 $a University of California, Santa Barbara. $b Mathematics. $3 2101287
773 0 $t Dissertations Abstracts International $g 85-02B.
790 $a 0035
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30530124