國立虎尾科技大學 |

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration/ by Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas.
作者:	Zamora Saiz, Alfonso.
其他作者:	Zúñiga-Rojas, Ronald A.
面頁冊數:	XIII, 127 p. 16 illus., 12 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematical Methods in Physics. -
電子資源:	https://doi.org/10.1007/978-3-030-67829-6
ISBN:	9783030678296

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
Zamora Saiz, Alfonso.

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration[electronic resource] /by Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas. - 1st ed. 2021. - XIII, 127 p. 16 illus., 12 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8201. - SpringerBriefs in Mathematics,.

Preface -- Introduction -- Preliminaries -- Geometric Invariant Theory -- Moduli Space of Vector Bundles -- Unstability Correspondence -- Stratifications on the Moduli Space of Higgs Bundles -- References -- Index.

This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.

ISBN: 9783030678296

Standard No.: 10.1007/978-3-030-67829-6doiSubjects--Topical Terms:

670749
Mathematical Methods in Physics.

LC Class. No.: QA564-609

Dewey Class. No.: 516.35

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
LDR:02891nam a22003975i 4500 001 1045591
003 DE-He213
005 20211125044517.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030678296 $9 978-3-030-67829-6
024 7 $a 10.1007/978-3-030-67829-6 $2 doi
035 $a 978-3-030-67829-6
050 4 $a QA564-609
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
100 1 $a Zamora Saiz, Alfonso. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1325527
245 1 0 $a Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration $h [electronic resource] / $c by Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XIII, 127 p. 16 illus., 12 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Mathematics, $x 2191-8201
505 0 $a Preface -- Introduction -- Preliminaries -- Geometric Invariant Theory -- Moduli Space of Vector Bundles -- Unstability Correspondence -- Stratifications on the Moduli Space of Higgs Bundles -- References -- Index.
520 $a This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
650 2 4 $a Mathematical Methods in Physics. $3 670749
650 1 4 $a Algebraic Geometry. $3 670184
650 0 $a Physics. $3 564049
650 0 $a Algebraic geometry. $3 1255324
700 1 $a Zúñiga-Rojas, Ronald A. $e author. $1 https://orcid.org/0000-0003-3402-2526 $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1348997
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030678289
776 0 8 $i Printed edition: $z 9783030678302
830 0 $a SpringerBriefs in Mathematics, $x 2191-8198 $3 1255329
856 4 0 $u https://doi.org/10.1007/978-3-030-67829-6
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)