26 citations · 77 across the 28 of their papers we have counts for
21 papers · 1 filter
On superspecial hyperelliptic curves of genus 5 whose automorphism groups contain
Ryo Ohashi, Momonari Kudo
While the numbers of superspecial curves of genus at most 3 are well understood, and several computational approaches have been developed to count superspecial curves of genus 4 wi…
Listing superspecial curves of genus three using Richelot isogeny graphs
Ryo Ohashi, Hiroshi Onuki, Momonari Kudo +2
In algebraic geometry, superspecial curves are important research objects. While the number of superspecial genus-3 curves in characteristic is known, the number of hyperellipt…
Explicit construction of a plane sextic model for genus-five Howe curves, II
Momonari Kudo
A Howe curve is defined as the normalization of the fiber product over a projective line of two hyperelliptic curves. Howe curves are very useful to produce important classes of cu…
Computing superspecial hyperelliptic curves of genus 4 with automorphism group properly containing the Klein 4-group
Ryo Ohashi, Momonari Kudo
In algebraic geometry, enumerating or finding superspecial curves in positive characteristic is important both in theory and in computation. In this paper, we propose feasible…
Explicit construction of a plane sextic model for genus-five Howe curves, I
Tomoki Moriya, Momonari Kudo
In the past several years, Howe curves have been studied actively in the field of algebraic curves over fields of positive characteristic. Here, a Howe curve is defined as the desi…
Efficient search for superspecial hyperelliptic curves of genus four with automorphism group containing
Momonari Kudo, Tasuku Nakagawa, Tsuyoshi Takagi
In arithmetic and algebraic geometry, superspecial (s.sp.\ for short) curves are one of the most important objects to be studied, with applications to cryptography and coding theor…
Some explicit arithmetic on curves of genus three and their applications
Tomoki Moriya, Momonari Kudo
A Richelot isogeny between Jacobian varieties is an isogeny whose kernel is included in the -torsion subgroup of the domain. A Richelot isogeny whose codomain is the product of…
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…
Counting isomorphism classes of superspecial curves
Momonari Kudo
A superspecial curve is a (non-singular) curve over a field of positive characteristic whose Jacobian variety is isomorphic to a product of supersingular elliptic curves over the 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…
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…
A note on certain superspecial and maximal curves of genus
Momonari Kudo
In this note, we characterize certain maximal superspecial curves of genus over finite fields. Specifically, we prove that the desingularization of $x y z^3 + x^5 + y^5 =…
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…
On the existence of superspecial nonhyperelliptic curves of genus
Momonari Kudo
A curve over a perfect field of characteristic is said to be superspecial if its Jacobian is isomorphic to a product of supersingular elliptic curves over the algebraic…
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…
Computing representation matrices for the action of Frobenius to cohomology groups
Momonari Kudo
This paper is concerned with the computation of representation matrices for the action of Frobenius to the cohomology groups of algebraic varieties. Specifically we shall give an a…
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…