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Dormant opers and Gauss maps in positive characteristic
Yasuhiro Wakabayashi
The Gauss map of a given projective variety is the rational map that sends a smooth point to the tangent space at that point, considered as a point of the Grassmann variety. The pr…
Arithmetic liftings and 2d TQFT for dormant opers of higher level
Yasuhiro Wakabayashi
This manuscript represents an advance in the enumerative geometry of opers that takes the subject beyond our previous work. Motivated by a counting problem of linear differential e…
Differential modules and dormant opers of higher level
Yasuhiro Wakabayashi
In the first half of the present paper, we study higher-level generalizations of differential modules in positive characteristic. These objects may be regarded as ring-theoretic co…
An upper bound on the generic degree of the generalized Verschiebung for rank two stable bundles
Yuichiro Hoshi, Yasuhiro Wakabayashi
In the present paper, we give an upper bound for the generic degree of the generalized Verschiebung between the moduli spaces of rank two stable bundles with trivial determinant.
Frobenius-Ehresmann structures and Cartan geometries in positive characteristic
Yasuhiro Wakabayashi
The aim of the present paper is to lay the foundation for a theory of Ehresmann structures in positive characteristic, generalizing the Frobenius-projective and Frobenius-affine st…
Projective and affine structures in positive characteristic I: Chern class formulas and Characterizations of projective spaces
Yasuhiro Wakabayashi
This paper aims to develop a theory of projective and affine structures on higher-dimensional varieties in positive characteristic. This theory deals with Frobenius-projective and…