Related papers: Reciprocity sheaves, II
We consider a notion of stability for sheaves, which we call multi-Gieseker stability that depends on several ample polarisations $L_1, \dots, L_N$ and on an additional parameter $\sigma \in \mathbb{Q}_{\geq 0}^N\setminus\{0\}$. The set of…
This short note contains an elementary observation in response to the recent posting arXiv:1707.06593v1, which studies the Lipschitz extension modulus to $n$ additional points. We bound this modulus in terms of the well-studied Lipschitz…
In this paper we study equivariant moduli spaces of sheaves on a $ K3 $ surface $ X $ under a symplectic action of a finite group. We prove that under some mild conditions, equivariant moduli spaces of sheaves on $ X $ are irreducible…
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology…
In the 1980s Dr\'ezet and Le Potier realized moduli spaces of Gieseker-semistable sheaves on $\mathbb{P}^2$ as what are now called quiver moduli spaces. We discuss how this construction can be understood using t-structures and exceptional…
We investigate the moduli spaces of one- and two-dimensional sheaves on projective K3 and abelian surfaces that are semistable with respect to a nongeneral ample divisor with regard to the symplectic resolvability. We can exclude the…
We prove a universal property for the $(\infty, n)$-category of correspondences, generalizing and providing a new proof for the case $n = 2$ from [GR17]. We also provide conditions under which a functor out of a higher category of…
This paper studies the intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$ -elliptic sheaves in the higher-rank setting, where $\mathcal{D}$ is a "maximal order" in a central division algebra $D$ over a global…
We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.
We show that the complement of arithmetic modular links found in arXiv:2307.09409 is homeomorphic to the complement of augmented chainlinks. In particular, these link complements arise as n-fold cyclic covers of the Whitehead link…
A construction of braid group actions on coherent sheaves using mixed Hodge modules and some well known constructions from geometric representation theory is given.
We give an elementary construction of homology of sheaves from Brown representability for the dual and see how its main properties are derived easily from the construction. Comparison with Poincar\'e-Verdier duality and with homology of…
Technical systems have evolved over time into large and complex Interwoven Systems consisting of several to a huge number of (possibly heterogeneous) subsystems that have interdependencies. The resultant mutual influences among subsystems…
We discuss the naive duality theory of coherent, torsion free, $S_2$ sheaves on schemes. Version 2: A solution of the original Conjecture 6.2 is added as an appendix by Hailong Dao.
We construct natural equivalences between derived categories of coherent sheaves on the local models for stratified Mukai or Atiyah flops (of type A).
This is a comment on two recent arXiv postings.
We study a class of semistability conditions defined by a system of ample classes for coherent sheaves over a smooth projective variety. Under some necessary boundedness assumptions, we show the existence of a well-behaved chamber structure…
We relate the endomorphism rings of certain $D$-elliptic sheaves of finite characteristic to hereditary orders in central division algebras over function fields.
This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two such moduli spaces of the same dimension…
We consider the set of affine alcoves associated with a root system R as a topological space and consider a certain category S of sheaves of Z-modules on this space. Here Z is the structure algebra of the root system over a field k. To any…