18 citations · 73 across the 19 of their papers we have counts for
19 papers
The Weil Decoration of the Horrocks-Mumford Bundle
Klaus Altmann, Andreas Hochenegger, Frederik Witt
For a normal algebraic variety we generalise the relation between reflexive rank one sheaves and Weil divisors to reflexive sheaves of arbitrary rank and so-called Weil decorations…
Toric sheaves and polyhedra
Klaus Altmann, Andreas Hochenegger, Frederik Witt
Over a smooth projective toric variety we study toric sheaves, that is, reflexive sheaves equivariant with respect to the acting torus, from a polyhedral point of view. One applica…
Exceptional sequences of line bundles on projective bundles
Klaus Altmann, Andreas Hochenegger, Frederik Witt
For a vector bundle we investigate exceptional sequences of line bundles on the total space of the projectivisation . In…
Asymmetry of -Functors
Andreas Hochenegger, Andreas Krug
Recently, a new definition of -functors was proposed by Anno and Logvinenko. In their article, the authors wonder whether this notion is symmetric in the sense that the…
Relations among -Twists
Andreas Hochenegger, Andreas Krug
Given two -objects in some algebraic triangulated category, we investigate the possible relations among the associated -twists. The main result is that, und…
Rationalizability of field extensions with a view towards Feynman integrals
Dino Festi, Andreas Hochenegger
In 2021, Marco Besier and the first author introduced the concept of rationalizability of square roots to simplify arguments of Feynman integrals. In this work, we generalize the d…
On Ulrich bundles on projective bundles
Andreas Hochenegger
In this article, the existence of Ulrich bundles on projective bundles is discussed. In the case, that the base variety is a curve or surface, a close rela…
Cox rings of algebraic stacks
Andreas Hochenegger, Elena Martinengo, Fabio Tonini
We give a proper definition of the multiplicative structure of the following rings: the Cox ring of invertible sheaves on a general algebraic stack; and the Cox ring of rank one re…
Frobenius and spherical codomains and neighbourhoods
Andreas Hochenegger, Ciaran Meachan
Given an exact functor between triangulated categories which admits both adjoints and whose cotwist is either zero or an autoequivalence, we show how to associate a unique full tri…
Introduction to derived categories of coherent sheaves
Andreas Hochenegger
In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective varie…
Formality of -objects
Andreas Hochenegger, Andreas Krug
We show that a -object and simple configurations of -objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) gener…
Maps of Mori dream spaces
Andreas Hochenegger, Elena Martinengo
Given a map of -factorial Mori dream spaces, one can ask whether this map is induced by a homogeneous homomorphism of Cox rings. As soon as…
Spherical subcategories in representation theory
Andreas Hochenegger, Martin Kalck, David Ploog
We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality…
Mori Dream Stacks
Andreas Hochenegger, Elena Martinengo
We propose a generalisation of Mori dream spaces to stacks. We show that this notion is preserved under root constructions and taking abelian gerbes. Unlike the case of Mori dream…
Spherical subcategories in algebraic geometry
Andreas Hochenegger, Martin Kalck, David Ploog
We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subc…
Exceptional Sequences of Line Bundles and Spherical Twists - a Toric Example
Andreas Hochenegger
Exceptional sequences of line bundles on a smooth projective toric surface are automatically full when they can be constructed via augmentation. By using spherical twists, we give…
Exceptional Sequences on Rational C*-Surfaces
Andreas Hochenegger, Nathan Owen Ilten
Inspired by Bondal's conjecture, we study the behavior of exceptional sequences of line bundles on rational C*-surfaces under homogeneous degenerations. In particular, we provide a…
On complex and symplectic toric stacks
Andreas Hochenegger, Frederik Witt
Toric varieties play an important role both in symplectic and complex geometry. In symplectic geometry, the construction of a symplectic toric manifold from a smooth polytope is du…
Families of Invariant Divisors on Rational Complexity-One T-Varieties
Andreas Hochenegger, Nathan Owen Ilten
We study invariant divisors on the total spaces of the homogeneous deformations of rational complexity-one T-varieties constructed by Ilten and Vollmert. In particular, we identify…