Integrable Systems and Torelli Theorems for the Moduli Spaces of Parabolic Bundles and Parabolic Higgs Bundles

被引：3

作者：

Biswas, Indranil ^{[1
]}

Gomez, Tomas L. ^{[2
]}

Logares, Marina ^{[2
]}

机构：

[1] Tata Inst Fundamental Res, Sch Math, Homi Bhabha Rd, Bombay 400005, Maharashtra, India

[2] CSIC UAM UC3M UCM, Inst Ciencias Matemat, C Nicolas Cabrera 15, Madrid 28049, Spain

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2016年 / 68卷 / 03期

关键词：

parabolic bundle; Higgs field; Torelli theorem; VECTOR-BUNDLES; CURVES;

D O I：

10.4153/CJM-2015-039-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight system is generic. When the genus is at least two, using this result we also prove a Torelli theorem for the moduli space of semistable parabolic bundles of rank at least two with generic parabolic weights. The key input in the proofs is a method of J.C. Hurtubise.

引用

页码：504 / 520

页数：17

共 50 条

[41] Betti numbers of the moduli space of rank 3 parabolic Higgs bundles
Garcia-Prada, O.
Gothen, P. B.
Munoz, V.
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 187 (879) : 1 - +
[42] QUASI-PARABOLIC HIGGS BUNDLES AND NULL HYPERPOLYGON SPACES
Godinho, Leonor
Mandini, Alessia
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 374 (10) : 7411 - 7447
[43] MODULI OF PARABOLIC G-BUNDLES
BHOSLE, UN
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 20 (01) : 45 - 48
[44] Bogomolov inequality for Higgs parabolic bundles
B. Anchouche
manuscripta mathematica, 1999, 100 : 423 - 436
[45] Bogomolov inequality for Higgs parabolic bundles
Anchouche, B
MANUSCRIPTA MATHEMATICA, 1999, 100 (04) : 423 - 436
[46] Geometry of moduli spaces of Higgs bundles
Biswas, Indranil
Schumacher, Georg
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2006, 14 (04) : 765 - 793
[47] Pullback and Direct Image of Parabolic Connections and Parabolic Higgs Bundles
Alfaya, David
Biswas, Indranil
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (22) : 19546 - 19591
[48] Asymptotic geometry of the moduli space of parabolic SL(2, C)-Higgs bundles
Fredrickson, Laura
Mazzeo, Rafe
Swoboda, Jan
Weiss, Hartmut
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2022, 106 (02): : 590 - 661
[49] Hodge classes of moduli spaces of parabolic bundles over the general curve
Biswas, I
Narasimhan, MS
JOURNAL OF ALGEBRAIC GEOMETRY, 1997, 6 (04) : 697 - 715
[50] The first Chern form on moduli of parabolic bundles
Takhtajan, Leon A.
Zograf, Peter
MATHEMATISCHE ANNALEN, 2008, 341 (01) : 113 - 135

← 1 2 3 4 5 →