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Geometric study of the category of m...

Yu, Xuan.

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Geometric study of the category of matrix factorizations.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Geometric study of the category of matrix factorizations./
Author:	Yu, Xuan.
Description:	87 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.
Contained By:	Dissertation Abstracts International74-11B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3588427
ISBN:	9781303264740

Geometric study of the category of matrix factorizations.
Yu, Xuan.

Geometric study of the category of matrix factorizations. - 87 p.

Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.

Thesis (Ph.D.)--The University of Nebraska - Lincoln, 2013.

We study the geometry of matrix factorizations in this dissertation. It contains two parts. The first one is a Chern-Weil style construction for the Chern character of matrix factorizations; this allows us to reproduce the Chern character in an explicit, understandable way. Some basic properties of the Chern character are also proved (via this construction) such as functoriality and that it determines a ring homomorphism from the Grothendieck group of matrix factorizations to its Hochschild homology. The second part is a reconstruction theorem of hypersurface singularities. This is given by applying a slightly modified version of Balmer's tensor triangular geometry to the homotopy category of matrix factorizations.

ISBN: 9781303264740Subjects--Topical Terms:

515831
Mathematics.

Geometric study of the category of matrix factorizations.
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005 20141010092813.5
008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781303264740
035 $a (MiAaPQ)AAI3588427
035 $a AAI3588427
040 $a MiAaPQ $c MiAaPQ
100 1 $a Yu, Xuan. $3 1265787
245 1 0 $a Geometric study of the category of matrix factorizations.
300 $a 87 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.
500 $a Adviser: Mark E. Walker.
502 $a Thesis (Ph.D.)--The University of Nebraska - Lincoln, 2013.
520 $a We study the geometry of matrix factorizations in this dissertation. It contains two parts. The first one is a Chern-Weil style construction for the Chern character of matrix factorizations; this allows us to reproduce the Chern character in an explicit, understandable way. Some basic properties of the Chern character are also proved (via this construction) such as functoriality and that it determines a ring homomorphism from the Grothendieck group of matrix factorizations to its Hochschild homology. The second part is a reconstruction theorem of hypersurface singularities. This is given by applying a slightly modified version of Balmer's tensor triangular geometry to the homotopy category of matrix factorizations.
590 $a School code: 0138.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a The University of Nebraska - Lincoln. $b Mathematics. $3 1030689
773 0 $t Dissertation Abstracts International $g 74-11B(E).
790 $a 0138
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3588427