Search results for "Mathematics::Commutative Algebra"
showing 10 items of 90 documents
Cocharacters of group graded algebras and multiplicities bounded by one
2017
Let G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the (Formula presented.)-ideals (Formula presented.) of graded identities of A such that the multiplicities (Formula presented.) in the graded cocharacter of A are bounded by one. We do so by exhibiting a set of identities of the (Formula presented.)-ideal. As a consequence we characterize the varieties of G-graded algebras whose lattice of subvarieties is distributive.
Ulrich bundles on K3 surfaces
2019
We show that any polarized K3 surface supports special Ulrich bundles of rank 2.
The associated graded module of the test module filtration
2017
We show that each direct summand of the associated graded module of the test module filtration $\tau(M, f^\lambda)_{\lambda \geq 0}$ admits a natural Cartier structure. If $\lambda$ is an $F$-jumping number, then this Cartier structure is nilpotent on $\tau(M, f^{\lambda -\varepsilon})/\tau(M, f^\lambda)$ if and only if the denominator of $\lambda$ is divisible by $p$. We also show that these Cartier structures coincide with certain Cartier structures that are obtained by considering certain $\mathcal{D}$-modules associated to $M$ that were used to construct Bernstein-Sato polynomials. Moreover, we point out that the zeros of the Bernstein-Sato polynomial $b_{M,f}$ attached to an \emph{$F$-…
Special arrangements of lines: Codimension 2 ACM varieties in P 1 × P 1 × P 1
2019
In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.
Complexity of gauge bounded Cartier algebras
2019
We show that a gauge bounded Cartier algebra has finite complexity. We also give an example showing that the converse does not hold in general.Communicated by Graham J. Leuschke
Effectively Computing Integral Points on the Moduli of Smooth Quartic Curves
2016
We prove an effective version of the Shafarevich conjecture (as proven by Faltings) for smooth quartic curves. To do so, we establish an effective version of Scholl's finiteness result for smooth del Pezzo surfaces of degree at most four.
Projective resolutions associated to projections
2000
In this paper we will describe projective resolutions of d dimensional Cohen–Macaulay spaces X by means of a projection of X to a hypersurface in d+1-dimensional space. We will show that for a certain class of projections, the resulting resolution is minimal.
From Bi-ideals to Periodicity
2008
The necessary and sufficient conditions are extracted for periodicity of bi-ideals. They cover infinitely and finitely generated bi-ideals.
Orbit spaces of Small Tori
2003
Consider an algebraic torus of small dimension acting on an open subset of ℂn, or more generally on a quasiaffine variety such that a separated orbit space exists. We discuss under which conditions this orbit space is quasiprojective. One of our counterexamples provides a toric variety with enough effective invariant Cartier divisors that is not embeddable into a smooth toric variety.
On cubic elliptic varieties
2013
Let X->P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.