The degree of the dormant operatic locus

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Let X be a smooth, projective curve of genus g ≥ 2 over an algebraically closed field of characteristic p > 0. I provide a conjectural formula for the degree of the scheme of dormant Projective General Linear PGL(r)-opers on X where r ≥ 2 (I assume that p is greater than an explicit constant depending on g, r). For r = 2, a dormant PGL(2)-oper is a dormant indigenous bundle on X in the sense of Shinichi Mochuzki (and his work provides a formula only for g = 2, r = 2, p ≥ 5, from a different point of view). In 2014, Yasuhiro Wakabayashi has shown that my conjectural formula holds for r = 2, g ≥ 2, and p > 2g - 2 and more recently he has proved the conjecture in all ranks for generic curves of genus at least two.

Original languageEnglish (US)
Pages (from-to)2599-2613
Number of pages15
JournalInternational Mathematics Research Notices
Volume2017
Issue number9
DOIs
StatePublished - May 1 2017

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'The degree of the dormant operatic locus'. Together they form a unique fingerprint.

  • Cite this