Related papers: Orientable 4-dimensional Poincar\'e Complexes have…

We prove an analogue of the result of Hsiang and Kleiner for 4-dimensional compact orbifolds with positive curvature and an isometric circle action. Additionally, we prove that when the underlying space is simply connected, then the…

The algorithm for inverting covariant exterior derivative is provided. It works for a sufficiently small star-shaped region of a fibered set - a local subset of a vector bundle and associated vector bundle. The algorithm contains some…

Abstract. Let G be a complex reductive group and A be an Abelian variety of dimension d over $\mathbb{C}$. We determine the Poincar\'e polynomials and also the mixed Hodge polynomials of the moduli space $\mathcal{M}_{A}^{H}(G)$ of G-Higgs…

A new compactification for the scheme of moduli for Gieseker-stable vector bundles with prescribed Hilbert polynomial, on the smooth projective polarized surface (S,L), is constructed. Families of locally free sheaves on the surface S are…

We give examples of stable rank 2 vector bundles on principally polarized abelian threefolds, and study their deformations. The starting point is the Serre construction, which gives a source of examples, and which we rephrase in terms of…

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.

Let $C$ be a curve with two smooth components and a single node. Let $\mathcal{U}_C(r,w,\chi)$ be the moduli space of $w$-semistable classes of depth one sheaves on $C$ having rank $r$ on both components and Euler characteristic $\chi$. In…

We show that the Poincare polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satisfies a topological recursion formula of the Eynard-Orantin type. The…

Let $f\colon X \dashrightarrow X$ be a birational transformation of a projective manifold $X$ whose Kodaira dimension $\kappa(X)$ is non-negative. We show that, if there exist a meromorphic fibration $\pi \colon X\dashrightarrow B$ and a…

In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…

Frames in finite-dimensional vector spaces are spanning sets of vectors which provide redundant representations of signals. The Parseval frames are particularly useful and important, since they provide a simple reconstruction scheme and are…

There is a canonical identification, due to the author, of a convex real projective structure on an orientable surface of genus g and a pair consisting of a conformal structure together with a holomorphic cubic differential on the surface.…

In this paper we investigate the problem of the cohomological classification of "Quaternionic" vector bundles in low-dimension ($d\leqslant 3$). We show that there exists a characteristic classes $\kappa$, called the FKMM-invariant, which…

We consider a proper flat fibration with real base and complex fibers. First we construct odd characteristic classes for such fibrations by a method that generalizes constructions of Bismut-Lott. Then we consider the direct image of a…

We define functorial isomorphisms of parallel transport along etale paths for a class of vector bundles on a p-adic curve. All bundles of degree zero whose reduction is strongly semistable belong to this class. In particular, they give rise…

We establish dimension formulas for the Witt vector affine Springer fibers associated to a reductive group over a mixed characteristic local field, under the assumption that the group is essentially tamely ramified and the residue…

In this paper, we study rational sections of the relative Picard scheme of a linear system on a smooth projective variety. We prove that if the linear system is basepoint-free and the locus of non-integral divisors has codimension at least…

"Quaternionic" vector bundles are the objects which describe the topological phases of quantum systems subjected to an odd time-reversal symmetry (class AII). In this work we prove that the FKMM invariant provides the correct fundamental…

We provide a modular construction of the Laza--Sacc\`a--Voisin compactification of the intermediate Jacobian fibration of a cubic fourfold. Additionally, we construct infinitely many $20$-dimensional families of polarized hyper-K\"ahler…

We construct a Fourier--Mukai transform for smooth complex vector bundles $E$ over a torus bundle $\pi:M \to B,$ the vector bundles being endowed with various structures of increasing complexity. At a minimum, we consider vector bundles $E$…