Asian Journal of Mathematics

Volume 23 (2019)

Number 6

Semistable Higgs bundles on Calabi–Yau manifolds

Pages: 905 – 918

DOI: https://dx.doi.org/10.4310/AJM.2019.v23.n6.a1

Authors

U. Bruzzo (Scuola Internazionale Superiore di Studi Avanzati (SISSA) Trieste, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy; and the Arnold–Regge Center for Algebra, Geometry & Theoretical Physics, Torino, Italy)

V. Lanza (Instituto de Matemática, Estatística e Computação Científica (IMECC) and Departamento de Matemática, Universidade Estadual de Campinas, SP, Brazil)

A. Lo Giudice

Abstract

We provide a partial classification of semistable Higgs bundles over simply connected Calabi–Yau manifolds. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces.

Keywords

Higgs bundles, Bogomolov inequality, restriction to curves, K3 surfaces

2010 Mathematics Subject Classification

14F05, 14H60, 14J60

Full Text (PDF format)

Received 19 October 2017

Accepted 6 September 2018

Published 3 August 2020