Related papers: On the Kummer construction
We show that the higher direct images of smooth commutative group schemes from the Kummer log flat site to the classical flat site are torsion. For (1) smooth affine commutative schemes with geometrically connected fibers, (2) finite flat…
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We compute the local intersection cohomology of the irreducible components of varieties of complexes, by using Lusztig's geometric approach to quantum groups and explicit constructions of elements of Lusztig's canonical bases.
We build extensions of the arc rings, relate their centers to the cohomology rings of the Springer varieties, and categorify all level two representations of quantum sl(N).
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
We construct the moduli space of finite dimensional representations of generalized quivers for arbitrary connected complex reductive groups using Geometric Invariant Theory as well as Symplectic reduction methods. We explicit characterize…
For quadratic spaces which represent 1 there is a characterization of hermitian compositions in the language of algebras-with-involutions using the even Clifford algebra. We extend this notion to define a generalized composition based on…
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.
We describe a universal factorization for a functor with values in finite-dimensional measured algebras. More precisely we contruct the quantum automorphism group of this functor. This general recontruction result allows us to recapture a…
We have two parallel goals of this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the…
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…
We develop the basic properties of the higher commutator for congruence modular varieties.
In this article we study derived (auto)equivalences of generalized Kummer varieties $\mathrm{Kum}^n(A)$. We provide an answer to a question raised by Namikawa by showing that the generalized Kummer varieties $\mathrm{Kum}^n(A)$ and…
We give a method to find quartic Heisenberg invariant equations for Kummer varieties and we give some explicit examples. From these equations for g-dimensional Kummer varieties one obtains equations for the moduli space of g+1-dimensional…
We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…
Suppose we take an abelian group G and quotient it by the action of negation. What structure does the quotient K inherit from the group structure of G? We describe this structure (which we call the Kummer of G) in terms of a map from the…
It is known that holomorphic Poisson structures are closely related to theories of generalized K\"{a}hler geometry and bi-Hermitian structures. In this article, we introduce quantization of holomorphic Poisson structures which are closely…
We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside…
By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional quantum-to-classical transition.…