26 citations · 75 across the 18 of their papers we have counts for
19 papers
An explicit form of the standard conjecture of Hodge type for Hermitian varieties, with -adic applications
Shushi Harashita
Let be a nonsingular Hermitian variety of even dimension over a finite field, and let be the lattice spanned by the classes of its maximal totally isotropic linear subspace…
The multiplicity-one theorem for the superspeciality of curves of genus two
Shushi Harashita, Yuya Yamamoto
Igusa proved in 1958 that the polynomial determining the supersingularity of elliptic curve in Legendre form is separable. In this paper, we get an analogous result for curves of g…
Superspecial genus- double covers of elliptic curves
Takumi Ogasawara, Ryo Ohashi, Kosuke Sakata +1
In this paper we study genus- curves obtained as double covers of elliptic curves. Firstly we shall give explicit defining equations of such curves with explicit criterion for w…
The cycle class of the supersingular locus of principally polarized abelian varieties
Gerard van der Geer, Shushi Harashita
We prove a formula for the cycle class of the supersingular locus in the Chow ring with rational coefficients of the moduli space of principally polarized abelian varieties in char…
Genus-five hyperelliptic or trigonal curves with many rational points in characteristic three
Momonari Kudo, Shushi Harashita
The number , the maximal number of -rational points on curves over of genus is unknown, but it is known that . In this…
Computing the space of differential forms of a plane curve and its Cartier-Manin matrix
Momonari Kudo, Shushi Harashita
In this paper, we propose a feasible algorithm to give an explicit basis of the space of regular differential forms on the nonsingular projective model of any given plane algebraic…
The -numbers of non-hyperelliptic curves of genus 3 with cyclic automorphism group of order 6
Ryo Ohashi, Momonari Kudo, Shushi Harashita
In this paper, we study non-hyperelliptic curves of genus with cyclic automorphism group of order . Over an algebraically closed field of characteristic , such…
Differential forms on the curves associated to Appell-Lauricella hypergeometric series and the Cartier operator on them
Ryo Ohashi, Shushi Harashita
Archinard studied the curve over associated to an Appell-Lauricella hypergeometric series and differential forms on its desingularization. In this paper, firstly a…
Representation of non-special curves of genus 5 as plane sextic curves and its application to finding curves with many rational points
Momonari Kudo, Shushi Harashita
In algebraic geometry, it is important to provide effective parametrizations for families of curves, both in theory and in practice. In this paper, we present such an effective par…
Algorithms to enumerate superspecial Howe curves of genus 4
Momonari Kudo, Shushi Harashita, Everett W. Howe
A Howe curve is a curve of genus obtained as the fiber product of two genus- double covers of . In this paper, we present a simple algorithm for testing isomor…
Algorithm to enumerate superspecial Howe curves of genus
Momonari Kudo, Shushi Harashita
A Howe curve is a curve of genus obtained as the fiber product over of two elliptic curves. Any Howe curve is canonical. This paper provides an efficient algorit…
Algorithmic study of superspecial hyperelliptic curves over finite fields
Momonari Kudo, Shushi Harashita
This paper presents algorithmic approaches to study superspecial hyperelliptic curves. The algorithms proposed in this paper are: an algorithm to enumerate superspecial hyperellipt…
The existence of supersingular curves of genus 4 in arbitrary characteristic
Momonari Kudo, Shushi Harashita, Hayato Senda
We prove that there exists a supersingular nonsingular curve of genus in arbitrary characteristic . For we shall prove that the desingularization of a certain fiber pr…
Superspecial trigonal curves of genus
Momonari Kudo, Shushi Harashita
This paper provides an algorithm enumerating superspecial trigonal curves of genus over finite fields. Executing the algorithm over a computer algebra system Magma, we enumerat…
Automorphism groups of superspecial curves of genus over
Momonari Kudo, Shushi Harashita, Hayato Senda
In this paper, we explicitly determine the automorphism group of every nonhyperelliptic superspecial curve of genus over . Our algorithm determining automorphi…
Asymptotic formula of the number of Newton polygons
Shushi Harashita
In this paper, we enumerate Newton polygons asymptotically. The number of Newton polygons is computable by a simple recurrence equation, but unexpectedly the asymptotic formula of…
On specializations of minimal -divisible groups
Nobuhiro Higuchi, Shushi Harashita
In this paper, for any pair of Newton polygons with , we construct a concrete specialization from the minimal -divisible group of to the minimal -divis…
Enumerating superspecial curves of genus over prime fields
Momonari Kudo, Shushi Harashita
In this paper we enumerate nonhyperelliptic superspecial curves of genus over prime fields of characteristic . Our algorithm works for nonhyperelliptic curves over an…
Superspecial curves of genus in small characteristic
Momonari Kudo, Shushi Harashita
This paper contains a complete study of superspecial curves of genus in characteristic . We prove that there does not exist a superspecial curve of genus in charact…