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The Degree of the Dormant Operatic Locus.
- Source :
-
IMRN: International Mathematics Research Notices . May2017, Vol. 2017 Issue 9, p2599-2613. 15p. - Publication Year :
- 2017
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PROJECTIVE curves
*POLYNOMIALS
*MORPHISMS (Mathematics)
*MATHEMATICAL formulas
Subjects
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2017
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 123170098
- Full Text :
- https://doi.org/10.1093/imrn/rnw066