The degree of the dormant operatic locus

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2 Citations (Scopus)

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

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Locus
Genus
Curve
Algebraically closed
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  • Mathematics(all)

Cite this

The degree of the dormant operatic locus. / Joshi, Kirti N.

In: International Mathematics Research Notices, Vol. 2017, No. 9, 01.05.2017, p. 2599-2613.

Research output: Contribution to journalArticle

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