東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

Symplectic Involutions : = From Cubic Fourfolds to OG10 Type Manifolds.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Symplectic Involutions :/
其他題名:	From Cubic Fourfolds to OG10 Type Manifolds.
作者:	Marquand, Lisa.
面頁冊數:	1 online resource (97 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30422274click for full text (PQDT)
ISBN:	9798379567644

Symplectic Involutions : = From Cubic Fourfolds to OG10 Type Manifolds.
Marquand, Lisa.

Symplectic Involutions :From Cubic Fourfolds to OG10 Type Manifolds. - 1 online resource (97 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--State University of New York at Stony Brook, 2023.

Includes bibliographical references

Irreducible holomorphic symplectic (IHS) manifolds are one of the building blocks of Kahler manifolds with trivial first Chern class, but very few examples are known. One strategy for potentially producing new examples is to study the fixed locus of finite groups of symplectic birational transformations of the known examples. We classify symplectic birational involutions of IHS manifolds deformation equivalent to O'Grady's 10 dimensional example (OG10 type). In particular, we show that there are 6 possible involutions, classified by their action on the second cohomology. From a cubic fourfold V ⊂ ℙ5, one can construct a IHS manifolds of OG10 type, equipped with a Lagrangian fibration X → ℙ5 . Three of the possible symplectic involutions can be obtained via this construction; explicitly, one starts with a cubic fourfold admitting an involution that induces a symplectic birational involution of X. We complete the classification of involutions of a cubic fourfold Hodge theoretically, which is equivalent to identifying a sublattice A(V)prim ⊂ H4 (V, ℤ) spanned by classes of surfaces contained in such a cubic. As a byproduct, we show that cubic fourfolds with involutions exhibit the full range of behaviour with regards to rationality conjectures. In particular, a cubic fourfold V with an involution that fixes a plane P ⊂ V point-wise is rational.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379567644Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Birational transformationsIndex Terms--Genre/Form:

542853
Electronic books.

Symplectic Involutions : = From Cubic Fourfolds to OG10 Type Manifolds.
LDR:02768nmm a2200385K 4500 001 2357763
005 20230725053703.5
006 m o d
007 cr mn ---uuuuu
008 241011s2023 xx obm 000 0 eng d
020 $a 9798379567644
035 $a (MiAaPQ)AAI30422274
035 $a AAI30422274
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Marquand, Lisa. $3 3698293
245 1 0 $a Symplectic Involutions : $b From Cubic Fourfolds to OG10 Type Manifolds.
264 0 $c 2023
300 $a 1 online resource (97 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Laza, Radu.
502 $a Thesis (Ph.D.)--State University of New York at Stony Brook, 2023.
504 $a Includes bibliographical references
520 $a Irreducible holomorphic symplectic (IHS) manifolds are one of the building blocks of Kahler manifolds with trivial first Chern class, but very few examples are known. One strategy for potentially producing new examples is to study the fixed locus of finite groups of symplectic birational transformations of the known examples. We classify symplectic birational involutions of IHS manifolds deformation equivalent to O'Grady's 10 dimensional example (OG10 type). In particular, we show that there are 6 possible involutions, classified by their action on the second cohomology. From a cubic fourfold V ⊂ ℙ5, one can construct a IHS manifolds of OG10 type, equipped with a Lagrangian fibration X → ℙ5 . Three of the possible symplectic involutions can be obtained via this construction; explicitly, one starts with a cubic fourfold admitting an involution that induces a symplectic birational involution of X. We complete the classification of involutions of a cubic fourfold Hodge theoretically, which is equivalent to identifying a sublattice A(V)prim ⊂ H4 (V, ℤ) spanned by classes of surfaces contained in such a cubic. As a byproduct, we show that cubic fourfolds with involutions exhibit the full range of behaviour with regards to rationality conjectures. In particular, a cubic fourfold V with an involution that fixes a plane P ⊂ V point-wise is rational.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Birational transformations
653 $a Cubic fourfolds
653 $a Hyperkaehler manifolds
653 $a Irreducible holomorphic symplectic
653 $a Rationality
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a State University of New York at Stony Brook. $b Mathematics. $3 2096807
773 0 $t Dissertations Abstracts International $g 84-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30422274 $z click for full text (PQDT)