Related papers: (Topological) modular forms with level structures:…

We reconsider some older constructions of T-duality, based on automorphisms of the worldsheet operator algebra, in a modern context. It has been long known that at special points in the moduli space of torus compactifications, the target…

We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method…

In this paper, we study certain moduli spaces of vector bundles on the blowup of the projective plane in at least 10 very general points. Moduli spaces of sheaves on general type surfaces may be nonreduced, reducible and even disconnected.…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…

Let X be a projective smooth irreducible polarized variety over the field of complex numbers. Typical examples of wide extensions are vector bundles E that have a subsheaf F whose slope is much bigger than the slope of E/F, and such that F…

Given a smooth non-hyperelliptic prime Fano threefold X, we prove the existence of all rank 2 ACM vector bundles on X by deformation of semistable sheaves. We show that these bundles move in generically smooth components of the…

We study fundamental forms of algebraic varieties using the sheaves of principal parts of line bundles and establish a vanishing theorem for any order fundamental forms. We also give connection of fundamental forms with the higher order…

We establish some properties of the derived category of torus-equivariant coherent sheaves on a split toric stack bundle. Our main result is a semi-orthogonal decomposition of such a category.

In view of applications to the construction of moduli spaces of objects in algebraic supergeometry, we start a systematic study of stacks in that context. After defining a superstack as a stack over the \'etale site of superschemes, we…

In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological…

We consider a smooth Poisson affine variety with the trivial canonical bundle over complex numbers. For such a variety the deformation quantization algebra A_h enjoys the conditions of the Van den Bergh duality theorem and the corresponding…

We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil…

The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…

Generalising a seminal result of Epstein and Penner for cusped hyperbolic manifolds, Cooper and Long showed that each decorated strictly convex projective cusped manifold has a canonical cell decomposition. Penner used the former result to…

A procedure resolving a torsion-free coherent sheaf on a nonsingular $N$-dimensional projective algebraic variety into a locally free sheaf on a projective scheme of certain class is proposed. This is a higher-dimensional analog of the…

We study families of algebraic varieties parametrized by topological spaces and generalize some classical results such as Hilbert Nullstellensatz and primary decomposition of commutative rings. We show that there is an equivalence between…

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 context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…

Let M(v) be the moduli of stable sheaves on K3 surfaces X of Mukai vector v. If v is primitive, than it is expected that M(v) is deformation equivalent to some Hilbert scheme and weight two hogde structure can be described by H^*(X,Z).…

We study the topology of the moduli space of flat SU(2)-bundles over a nonorientable surface X. This moduli space may be identified with the space of homomorphisms Hom(\pi_1(X),SU(2)) modulo conjugation by SU(2). In particular, we compute…