16 citations · 27 across the 20 of their papers we have counts for
22 papers
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…
On the category of structure species
Yasuhiro Wakabayashi
The purpose of the present paper is to make a mathematical study of the differences and relations among possible structures inherent in an object, as well as of the whole structure…
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…
Quantization on Algebraic Curves with Frobenius-Projective Structure
Yasuhiro Wakabayashi
In the present paper, we study the relationship between deformation quantizations and Frobenius-projective structures defined on an algebraic curve in positive characteristic. A Fr…
An effective version of Belyi's theorem in positive characteristic
Yasuhiro Wakabayashi
The purpose of the present paper is to give an effective version of the noncritical -tame Belyi theorem. That is to say, we compute explicitly an upper bound of the minimal degr…
A combinatorial description of the dormant Miura transformation
Yasuhiro Wakabayashi
A dormant generic Miura -oper is a flat -bundle over an algebraic curve in positive characteristic equipped with some additional data. In the prese…
Symplectic geometry of -adic Teichmüller uniformization for ordinary nilpotent indigenous bundles
Yasuhiro Wakabayashi
The aim of the present paper is to provide a new aspect of the -adic Teichmüller theory established by S. Mochizuki. We study the symplectic geometry of the -adic formal stac…
Gaudin model modulo , Tango structures, and dormant Miura opers
Yasuhiro Wakabayashi
In the present paper, we study the Bethe ansatz equations for Gaudin model and Miura opers in characteristic . Our study is based on a work by E. Frenkel, in which solutions t…
Moduli of Tango structures and dormant Miura opers
Yasuhiro Wakabayashi
The purpose of the present paper is to develop the theory of (pre-)Tango structures and (dormant generic) Miura -opers (for a semisimple Lie algebra ) d…
Topological quantum field theory for dormant opers
Yasuhiro Wakabayashi
The purpose of the present paper is to develop the enumerative geometry of dormant -opers for a semisimple algebraic group . In the present paper, we construct a compact modu…
Categorical representation of superschemes
Yasuhiro Wakabayashi
In the present paper, we prove that a locally noetherian superscheme may be reconstructed (up to certain equivalence) category-theoretically from the category of noet…
Moduli of log twisted SUSY curves
Yasuhiro Wakabayashi
The goal of the present paper is to construct a smooth compactification of the moduli superstack classifying pointed SUSY (= ) curves. This construc…
Cyclic étale coverings of generic curves and ordinariness of dormant opers
Yasuhiro Wakabayashi
The ordinariness of elliptic curves is essential in proving various expected properties of elliptic curves in positive characteristic and can be extended to algebraic curves of arb…
On the cuspidalization problem for hyperbolic curves over finite fields
Yasuhiro Wakabayashi
In this paper, we study some group-theoretic constructions associated to arithmetic fundamental groups of hyperbolic curves over finite fields. One of the main results of this pape…
Duality for dormant opers
Yasuhiro Wakabayashi
In the present paper, we prove that on a fixed pointed stable curve of characteristic , there exists a duality between dormant -opers () and dorma…
An explicit formula for the generic number of dormant indigenous bundles
Yasuhiro Wakabayashi
A dormant indigenous bundle is an integrable projective line bundle on a proper hyperbolic curve of positive characteristic satisfying certain conditions. Dormant indigenous bundle…
A theory of dormant opers on pointed stable curves -- a proof of Joshi's conjecture
Yasuhiro Wakabayashi
This manuscript presents a detailed and original account of the theory of opers defined on pointed stable curves in arbitrary characteristic and their moduli. In particular, it inc…
The symplectic nature of the space of dormant indigenous bundles on algebraic curves
Yasuhiro Wakabayashi
We study the symplectic nature of the moduli stack classifying dormant curves over a field of positive characteristic, i.e., proper hyperbolic curves over equipped with a d…