System of Hodge bundles and generalized opers on smooth projective varieties

JOURNAL OF GEOMETRY AND PHYSICS

卷:145

Article

Basu, Suratno¹  Paul, Arjun²  Saha, Arideep¹ 

[1] Inst Math Sci, 4th Cross St,CIT Campus, Chennai 600113, Tamil Nadu, India

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

关键词: Generalized oper;    Griffiths transversal filtration;    Higgs bundle;    System of Hodge bundles;    Semistable bundle;   

DOI  :  10.1016/j.geomphys.2019.103484

来源: Elsevier

【 摘 要 】

Let k be an algebraically closed field of any characteristic. Let X be a polarized irreducible smooth projective algebraic variety over k. We give criterion for semistability and stability of system of Hodge bundles on X. We define notion of generalized opers on X, and prove semistability of the Higgs bundle associated to generalized opers. We also show that existence of partial oper structure on a vector bundle E together with a connection del over X implies semistability of the pair (E, del). (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free