Higgs bundles and fundamental group schemes

被引：4

作者：

Biswas, Indranil ^{[1
]}

Bruzzo, Ugo ^{[2
,3
]}

Gurjar, Sudarshan ^{[4
]}

机构：

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

[2] SISSA, Via Bonomea 265, I-34136 Trieste, Italy

[3] Ist Nazl Fis Nucl, Sez Trieste, Trieste, Italy

[4] Indian Inst Technol, Dept Math, Mumbai 400076, Maharashtra, India

来源：

ADVANCES IN GEOMETRY | 2019年 / 19卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

Higgs bundles; Tannakian category; numerically effectiveness; SEMISTABILITY;

D O I：

10.1515/advgeom-2018-0035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Relying on a notion of "numerical effectiveness" for Higgs bundles, we show that the category of "numerically flat" Higgs vector bundles on a smooth projective variety X is a Tannakian category. We introduce the associated group scheme, that we call the "Higgs fundamental group scheme of X," and show that its properties are related to a conjecture about the vanishing of the Chern classes of numerically flat Higgs vector bundles.

引用

页码：381 / 388

页数：8

共 50 条

[21] Perverse filtrations, Hilbert schemes, and the P = W conjecture for parabolic Higgs bundles
Shen, Junliang
Zhang, Zili
ALGEBRAIC GEOMETRY, 2021, 8 (04): : 465 - 489
[22] Fourier-Mukai transformation and logarithmic Higgs bundles on punctual Hilbert schemes
Biswas, Indranil
Krug, Andreas
JOURNAL OF GEOMETRY AND PHYSICS, 2020, 150
[23] HIGGS BUNDLES FOR THE NON-COMPACT DUAL OF THE UNITARY GROUP
Garcia-Prada, Oscar
Oliveira, Andre G.
ILLINOIS JOURNAL OF MATHEMATICS, 2011, 55 (03) : 1155 - 1181
[24] ACTION OF THE MAPPING CLASS GROUP ON CHARACTER VARIETIES AND HIGGS BUNDLES
Garcia-Prada, Oscar
Wilkin, Graeme
DOCUMENTA MATHEMATICA, 2020, 25 : 841 - 868
[25] Surface group representations and U(p, q)-Higgs bundles
Bradlow, SB
García-Prada, O
Gothen, PB
JOURNAL OF DIFFERENTIAL GEOMETRY, 2003, 64 (01) : 111 - 170
[26] Heights of vector bundles and the fundamental group scheme of a curve
Gasbarri, C
DUKE MATHEMATICAL JOURNAL, 2003, 117 (02) : 287 - 311
[27] Semistable bundles on curves and reducible representations of the fundamental group
Esnault, H
Hertling, C
INTERNATIONAL JOURNAL OF MATHEMATICS, 2001, 12 (07) : 847 - 855
[28] VECTOR BUNDLES ON CURVES AND REPRESENTATIONS OF ALGEBRAIC FUNDAMENTAL GROUP
LANGE, H
STUHLER, U
MATHEMATISCHE ZEITSCHRIFT, 1977, 156 (01) : 73 - 83
[29] ON THE FUNDAMENTAL GROUP SCHEMES OF CERTAIN QUOTIENT VARIETIES
Biswas, Indranil
Hai, Phung Ho
dos Santos, Joao Pedro
TOHOKU MATHEMATICAL JOURNAL, 2021, 73 (04) : 565 - 595
[30] Fundamental group schemes of generalized Kummer variety
Rasul, Parvez
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2023, 133 (02):

← 1 2 3 4 5 →