arXiv subjects

Axel Stäbler

Publications and source records attributed to Axel Stäbler.

23 records · Page 2Linked to original sources

arXiv2012

On the behaviour of strong semistability in geometric deformations

Let $Y \to B$ be a relative smooth projective curve over an affine integral base scheme $B$ of positive characteristic. We provide for all prime characteristics example classes of vector bundles $\mathcal{S}$ over $Y$ such that $\mathcal{S}$ is generically strongly semistable and semistable but not strongly semistable for some special fibre. This also provides new examples of the behaviour of Hilbert-Kunz multiplicities in geometric families.

math.AG↗

arXiv2012

Dagger closure in regular rings containing a field

We prove that dagger closure is trivial in regular domains containing a field and that graded dagger closure is trivial in polynomial rings over a field. We also prove that Heitmann's full rank one closure coincides with tight closure in positive characteristic under some mild finiteness conditions. Furthermore, we prove that dagger closure is always contained in solid closure and that the forcing algebra for an element contained in dagger closure is parasolid.

math.AC↗

arXiv2011

An inclusion result for dagger closure in certain section rings of abelian varieties

We prove an inclusion result for graded dagger closure for primary ideals in symmetric section rings of abelian varieties over an algebraically closed field of arbitrary characteristic.

math.AC↗

arXiv2011

An explicit computation of a family of trivialising étale covers

We explicitly compute étale covers of the smooth Fermat curves $Y_{p+1} = \Proj k[u,v,w]/(u^{p+1} + v^{p+1} - w^{p+1})$ which trivialise the vector bundles $\Syz(u^2, v^2, w^2)(3)$, where $k$ is a field of characteristic $p \geq 3$.

math.AG↗

arXiv2011

Dagger closure and solid closure in graded dimension two

We introduce a graded version of dagger closure and prove that it coincides with solid closure for homogeneous ideals in two dimensional $\mathbb{N}$-graded domains of finite type over a field.

math.AG↗