arXiv subjects

Andreas Steffens

Publications and source records attributed to Andreas Steffens.

3 recordsLinked to original sources

arXiv1996

Bounds for Seshadri Constants

In the paper we present an alternative approach to the boundedness of Seshadri constants (which measure the local positivity) of nef and big line bundles at a general point of a complex--projective variety. Our approach is based on the construction of divisors in certain adjoint linear systems having isolated singularities of high order. A variant of the method gives bounds for Seshadri constants valid at arbitrary points of a smooth variety; these bounds, however, depend on the line bundle and the positivity of the tangent bundle of the variety in question.

alg-geom↗

arXiv1995

Remarks on Seshadri constants

Given a smooth complex projective variety $X$ and an ample line bundle $L$ on $X$. Fix a point $x\in X$. We consider the question, are there conditions which guarantee the maxima of the Seshadri constant of $L$ at $x$, i.e $\eps(L,x)=\root n \of {L^n}$? We give a partial answer for surfaces and find examples where the answer to our question is negative. If $(X,Θ)$ is a general principal polarized abelian surface, then $\eps(Θ,x)={4/3}<\sqrt{2}=\sqrt{Θ^2}$ for all $x\in X$.

alg-geom↗

arXiv1994

On the stability of the tangent bundle of Fano manifolds

By using the classification of Fano 3-folds we prove: Let $X$ be Fano 3-fold. Assume that the tangent bundle $T_X$ of $X$ is not stable (i.e. semi-stable or unstable). Then $b_2\geq 2$ and a relative tangent sheaf $T_{X/Y}$ of a contraction $f:X\longrightarrow Y$ of an extremal face on $X$ is a destabilising subsheaf of $T_X$.

alg-geom↗