Higgs bundles and fundamental group schemes-Reference-Cited by-同舟云学术

Higgs bundles and fundamental group schemes

Published:2019-06-21 Issue:3 Volume:19 Page:381-388
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Biswas Indranil¹,Bruzzo Ugo²³,Gurjar Sudarshan⁴

Affiliation:

1. School of Mathematics, Tata Institute of Fundamental Research , Homi Bhabha Road , Bombay , 400005 , India

2. Scuola Internazionale Superiore di Studi Avanzati (SISSA) , Via Bonomea 265, 34136 , Trieste , Italy

3. Istituto Nazionale di Fisica Nucleare , Sezione di Trieste , Trieste , Italy

4. Department of Mathematics , Indian Institute of Technology , Mumbai , 400076 , India

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2018-0035/pdf

Reference19 articles.

1. V. Balaji, A. J. Parameswaran, Tensor product theorem for Hitchin pairs —an algebraic approach. Ann. Inst. Fourier (Grenoble) 61 (2011), 2361–2403 (2012). MR2976315 Zbl 1248.14046

2. C. M. Barton, Tensor products of ample vector bundles in characteristic p. Amer. J. Math. 93 (1971), 429–438. MR0289525 Zbl 0221.14011

3. I. Biswas, U. Bruzzo, On semistable principal bundles over a complex projective manifold. Int. Math. Res. Not. 12 (2008), 28pp. MR2426752 Zbl 1183.14065

4. I. Biswas, Y. I. Holla, Semistability and numerically effectiveness in positive characteristic. Internat. J. Math. 22 (2011), 25–46. MR2765441 Zbl 1235.14041

5. U. Bruzzo, B. Graña Otero, Numerically flat Higgs vector bundles. Commun. Contemp. Math. 9 (2007), 437–446. MR2348839 Zbl 1152.14016

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