Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\le 7$

Abstract

This note studies ${\mathrm{PGL}}_n$-opers arising from generalized hypergeometric differential equations in prime characteristic $p$. We prove that these opers are rigid within the class of dormant opers. By combining this rigidity result with previous work in the enumerative geometry of dormant opers, we obtain a complete and explicit description of the $2$d TQFTs that compute the number of dormant ${\mathrm{PGL}}_n$-opers for primes $p\le 7$.

26 pages