arXiv subjects

Kyoji Saito

Publications and source records attributed to Kyoji Saito.

23 records · Page 2Linked to original sources

arXiv2009

Monoids in the fundamental groups of the complement of logarithmic free divisors in C^3

We study monoids generated by Zariski-van Kampen generators in the 17 fundamental groups of the complement of logarithmic free divisors in C^3 listed by Sekiguchi (Theorem 1). Five of them are Artin monoids and eight of them are free abelian monoids. The remaining four monoids are not Gaussian and, hence, are neither Garside nor Artin (Theorem 2). However, we introduce, similarly to Artin monoids, fundamental elements and show their existence (Theorem 3). One of the four non-Gaussian monoids satisfies the cancellation condition (Theorem 4).

math.GR↗

arXiv2007

Triangulated categories of matrix factorizations for regular systems of weights with $ε=-1$

We construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a non-degenerate regular system of weights whose smallest exponents are equal to -1. In the associated Grothendieck group, the strongly exceptional collection defines a root basis of a generalized root system of sign (l,0,2) and a Coxeter element of finite order, whose primitive eigenvector is a regular element in the expanded symmetric domain of type IV with respect to the Weyl group.

math.AG↗

arXiv2006

Matrix Factorizations and Representations of Quivers II: type ADE case

We study a triangulated category of graded matrix factorizations for a polynomial of type ADE. We show that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding Dynkin quiver. Also, we discuss a special stability condition for the triangulated category in the sense of T. Bridgeland, which is naturally defined by the grading.

math.AG↗

arXiv2006

Eta-product $η(7τ)^7/η(τ)$

The Dirichlet series associated to the eta-product $η(7τ)^7/η(τ)$ decomposes uniquely into the difference of two L-functions with Euler products. This expression gives a new proof of the positivity of the Fourier coefficients of the eta-product.

math.NT↗

arXiv2005

Principal $Γ$-cone for a tree

Each orientation on a Dynkin graph $Γ$ defines a cone (in a certain real configuration space) which is further divided into chambers. We enumerate the number of chambers for two particular cones, which are called the pricipal $Γ$-cones and are attached to bipartite decompositions of $Γ$, by a use of hook length formulae. We prove that these pricipal cones are characterized by the maximality of the number of chambers in them.

math.CO↗