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of 91
pro vyhledávání: '"Matsumoto, Yuya"'
Autor:
Matsumoto, Yuya
We introduce an inseparable version of Kummer surfaces. It is defined as a supersingular K3 surface in characteristic 2 with 16 smooth rational curves forming a certain configuration and satisfying a suitable divisibility condition. The main result i
Externí odkaz:
http://arxiv.org/abs/2403.02770
Autor:
Matsumoto, Yuya
Given an abelian surface $A$, defined over a discrete valuation field and having good reduction, does the attached Kummer surface $\mathrm{Km}(A)$ also have good reduction? In this paper we give an affirmative answer in the extreme case, that is, whe
Externí odkaz:
http://arxiv.org/abs/2302.09535
We study torsors under finite group schemes over the punctured spectrum of a singularity $x\in X$ in positive characteristic. We show that the Dieudonn\'e module of the (loc,loc)-part $\mathrm{Picloc}^{\mathrm{loc},\mathrm{loc}}_{X/k}$ of the local P
Externí odkaz:
http://arxiv.org/abs/2110.03650
We study isolated quotient singularities by finite and linearly reductive group schemes (lrq singularities for short) and show that they satisfy many, but not all, of the known properties of finite quotient singularities in characteristic zero: (1) F
Externí odkaz:
http://arxiv.org/abs/2102.01067
Autor:
Matsumoto, Yuya
Publikováno v:
J. Singul. 24 (2022), 79-95
We classify purely inseparable morphisms of degree $p$ between rational double points (RDPs) in characteristic $p > 0$. Using such morphisms, we refine a result of Artin that any RDP admits a finite smooth covering.
Comment: 16 pages, title slig
Comment: 16 pages, title slig
Externí odkaz:
http://arxiv.org/abs/2003.10344
Autor:
Matsumoto, Yuya
Publikováno v:
J. Commut. Algebra 15(3): 377-404 (Fall 2023)
We consider rational double point singularities (RDPs) that are non-taut, which means that the isomorphism class is not uniquely determined from the dual graph of the minimal resolution. Such RDPs exist in characteristic $2,3,5$. We compute the actio
Externí odkaz:
http://arxiv.org/abs/1907.04686
Autor:
Matsumoto, Yuya
Publikováno v:
Math. Soc. Japan 74 (3) 849 - 872, July, 2022
Let $\bar{Y}$ be a normal surface that is the canonical $\mu_2$- or $\alpha_2$-covering of a classical or supersingular Enriques surface in characteristic $2$. We determine all possible configurations of singularities on $\bar{Y}$, and for each confi
Externí odkaz:
http://arxiv.org/abs/1812.06914
Autor:
Matsumoto, Yuya
Publikováno v:
J. Algebraic Geom. 32 (2023), 271-322
We consider $\mu_p$- and $\alpha_p$-actions on RDP K3 surfaces (K3 surfaces with rational double point singularities allowed) in characteristic $p > 0$. We study possible characteristics, quotient surfaces, and quotient singularities. It turns out th
Externí odkaz:
http://arxiv.org/abs/1812.03466
Autor:
Matsumoto, Yuya
Publikováno v:
Nagoya Mathematical Journal, 249 (2023), 11-49
In characteristic $0$, symplectic automorphisms of K3 surfaces (i.e.\ automorphisms preserving the global $2$-form) and non-symplectic ones behave differently. In this paper we consider the actions of the group schemes $\mu_{n}$ on K3 surfaces (possi
Externí odkaz:
http://arxiv.org/abs/1710.07158
Publikováno v:
Mathematische Nachrichten 291 (2018), no. 13, 2084-2098
Consider an arbitrary automorphism of an Enriques surface with its lift to the covering K3 surface. We prove a bound of the order of the lift acting on the anti-invariant cohomology sublattice of the Enriques involution. We use it to obtain some mod
Externí odkaz:
http://arxiv.org/abs/1707.02563