Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Katsura, Toshiyuki"'
We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exception
Externí odkaz:
http://arxiv.org/abs/2410.14085
Autor:
Katsura, Toshiyuki, Schütt, Matthias
Publikováno v:
Ãpijournal de Géométrie Algébrique, Volume 8 (June 7, 2024) epiga:11410
We work out normal forms for quasi-elliptic Enriques surfaces and give several applications. These include torsors and numerically trivial automorphisms, but our main application is the completion of the classification of Enriques surfaces with finit
Externí odkaz:
http://arxiv.org/abs/2304.12599
Autor:
Katsura, Toshiyuki, Kondo, Shigeyuki
We give an analogue in characteristic 2 of the classical theory of quadric line complexes and Kummer surfaces.
Comment: 47 pages, 3 figures
Comment: 47 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/2301.01450
We advance previous studies on decomposed Richelot isogenies (Katsura--Takashima (ANTS 2020) and Katsura (ArXiv 2021)) which are useful for analysing superspecial Richelot isogeny graphs in cryptography. We first give a characterization of decomposed
Externí odkaz:
http://arxiv.org/abs/2108.06936
Autor:
Katsura, Toshiyuki, Kondo, Shigeyuki
We study Coble surfaces in characteristic 2, in particular, singularities of their canonical coverings. As an application we classify Coble surfaces with finite automorphism group in characteristic 2. There are exactly 9 types of such surfaces.
Externí odkaz:
http://arxiv.org/abs/2107.14537
Autor:
Katsura, Toshiyuki
For a nonsingular projective curve $C$ of genus 3 defined over an algebraically closed field of characteristic $p > 2$, we give a necessary and sufficient condition that the Jacobian variety $J(C)$ has a decomposed Richelot isogeny outgoing from it a
Externí odkaz:
http://arxiv.org/abs/2103.01800
Autor:
Katsura, Toshiyuki, Saito, Natsuo
We consider the multicanonical systems $\vert mK_{S}\vert$ of quasi-elliptic surfaces with Kodaira dimension $1$ in characteristic 2. We show that for any $m \geq 6$ $\vert mK_{S}\vert$ gives the structure of quasi-elliptic fiber space, and 6 is the
Externí odkaz:
http://arxiv.org/abs/2006.11959
Castryck, Decru, and Smith used superspecial genus-2 curves and their Richelot isogeny graph for basing genus-2 isogeny cryptography, and recently, Costello and Smith devised an improved isogeny path-finding algorithm in the genus-2 setting. In order
Externí odkaz:
http://arxiv.org/abs/2003.00633
Autor:
Katsura, Toshiyuki, Schütt, Matthias
We study K3 surfaces with 9 cusps, i.e. 9 disjoint $A_2$ configurations of smooth rational curves, over algebraically closed fields of characteristic $p\neq 3$. Much like in the complex situation studied by Barth, we prove that each such surface admi
Externí odkaz:
http://arxiv.org/abs/1902.01579
Autor:
Katsura, Toshiyuki, Schütt, Matthias
We construct Zariski K3 surfaces of Artin invariant 1, 2 and 3 in many characteristics. In particular, we prove that any supersingular Kummer surface is Zariski if the characteristic is not congruent to 1 modulo 12. Our methods combine different appr
Externí odkaz:
http://arxiv.org/abs/1710.08661