Zobrazeno 1 - 10
of 172
pro vyhledávání: '"Altmann, Klaus"'
For a vector bundle $\mathcal E \to \mathbb P^\ell$ we investigate exceptional sequences of line bundles on the total space of the projectivisation $X = \mathbb P(\mathcal E)$. In particular, we consider the case of the cotangent bundle of $\mathbb P
Externí odkaz:
http://arxiv.org/abs/2303.10924
Publikováno v:
Ãpijournal de Géométrie Algébrique, Volume 8 (May 12, 2024) epiga:11407
We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maximal rank. As an application, we construct a lattice polytope such that
Externí odkaz:
http://arxiv.org/abs/2209.06044
Autor:
Altmann, Klaus, Witt, Frederik
For a smooth projective toric variety of Picard rank two we classify all exceptional sequences of invertible sheaves which have maximal length. In particular, we prove that unlike non-maximal sequences, they (a) remain exceptional under lexicographic
Externí odkaz:
http://arxiv.org/abs/2112.14637
Autor:
Altmann, Klaus, Altmann, Martin
We investigate maximal exceptional sequences of line bundles on (P^1)^3, i.e. those consisting of 2^r elements. For r=3 we show that they are always full, meaning that they generate the derived category. Everything is done in the discrete setup: Exce
Externí odkaz:
http://arxiv.org/abs/2108.11806
For any two nef line bundles F and G on a toric variety X represented by lattice polyhedra P respectively Q, we present the universal equivariant extension of G by F under use of the connected components of the set theoretic difference of Q and P.
Externí odkaz:
http://arxiv.org/abs/2012.04590
We study deformations of affine toric varieties. The entire deformation theory of these singularities is encoded by the so-called versal deformation. The main goal of our paper is to construct the homogeneous part of some degree -R of this, i.e. a ma
Externí odkaz:
http://arxiv.org/abs/2005.01884
For an arbitrary rational polyhedron we consider its decompositions into Minkowski summands and, dual to this, the free extensions of the associated pair of semigroups. Being free for the pair of semigroups is equivalent to flatness for the correspon
Externí odkaz:
http://arxiv.org/abs/2004.07377
Autor:
Altmann, Klaus, Witt, Frederik
We characterise and investigate co-Higgs sheaves and associated algebraic and combinatorial invariants on toric varieties. In particular, we compute explicit examples.
Comment: 20 pages; final version
Comment: 20 pages; final version
Externí odkaz:
http://arxiv.org/abs/2004.03721
Autor:
Altmann, Klaus, Ploog, David
There is a standard method to calculate the cohomology of torus-invariant sheaves $L$ on a toric variety via the simplicial cohomology of associated subsets $V(L)$ of the space $N_{\mathbb R}$ of 1-parameter subgroups of the torus. For a line bundle
Externí odkaz:
http://arxiv.org/abs/1903.08009
We call a sheaf on an algebraic variety immaculate if it lacks any cohomology including the zero-th one, that is, if the derived version of the global section functor vanishes. Such sheaves are the basic tools when building exceptional sequences, inv
Externí odkaz:
http://arxiv.org/abs/1808.09312