17 research outputs found
Irreducibility criterion for algebroid curves
The purpose of this paper is to give an algorithm for deciding the
irreducibility of reduced algebroid curves over an algebraically closed field
of arbitrary characteristic. To do this, we introduce a new notion of local
tropical variety which is a straightforward extension of tropism introduced by
Maurer, and then give irreducibility criterion for algebroid curves in terms
local tropical varieties. We also give an algorithm for computing the
value-semigroups of irreducible algebroid curves. Combining the irreducibility
criterion and the algorithm for computing the value-semigroups, we obtain an
algorithm for deciding the irreducibility of algebroid curves.Comment: 20 pages, v3: major revisio
One-dimensional rings of finite F-representation type
We prove that a complete local or graded one-dimensional domain of prime
characteristic has finite F-representation type if its residue field is
algebraically closed or finite, and present examples of a complete local or
graded one-dimensional domain which does not have finite F-representation type
with a perfect residue field. We also present some examples of higher
dimensional rings of finite F-representation type.Comment: 8 pages, title changed and typos correcte
Toric ideals for high Veronese subrings of toric algebras
We prove that the defining ideal of a sufficiently high Veronese subring of a
toric algebra admits a quadratic Gr\"obner basis consisting of binomials. More
generally, we prove that the defining ideal of a sufficiently high Veronese
subring of a standard graded ring admits a quadratic Gr\"obner basis. We give a
lower bound on such that the defining ideal of -th Veronese subring
admits a quadratic Gr\"obner basis. Eisenbud--Reeves--Totaro stated the same
theorem without a proof with some lower bound on . In many cases, our lower
bound is less than Eisenbud--Reeves--Totaro's lower bound.Comment: 9 pages, v2: Observation 3.16 added and typos corrected, v3: typos
correcte
Algorithms for computing multiplier ideals
We give algorithms for computing multiplier ideals using Gr\"obner bases in
Weyl algebras. The algorithms are based on a newly introduced notion which is a
variant of Budur--Musta\c{t}\v{a}--Saito's (generalized) Bernstein--Sato
polynomial. We present several examples computed by our algorithms.Comment: 23 pages, title changed, Theorem 4.5 added, typos corrected, and some
minor revisions (some notation changed, and Definition 2.1, Proposition 2.11,
Observation 3.1, and Observation 4.2 added