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

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Equivalence Between Kuznetsov Components of Cubic Fourfolds and Gushel-Mukai Fourfolds./
Author:	Chen, Qingjing.
Description:	1 online resource (95 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
Contained By:	Dissertations Abstracts International85-02B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
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. - 1 online resource (95 pages)

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

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

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380158961Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Algebraic geometryIndex Terms--Genre/Form:

554714
Electronic books.

Equivalence Between Kuznetsov Components of Cubic Fourfolds and Gushel-Mukai Fourfolds.
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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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
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
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710 2 $a University of California, Santa Barbara. $b Mathematics. $3 1476121
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