Related papers: Zariski chambers, volumes, and stable base loci
In this note we introduce a construction which assigns to an arbitrary manifold bundle its fiberwise orientation covering. This is used to show that the zeta classes of unoriented surface bundles are not divisible in the stable range.
We experimentally investigate how a long granular pile confined in a narrow channel destabilizes when it is inclined above the angle of repose. A uniform flow then develops, which is localized at the free surface. It first accelerates…
In this paper, we study how certain vector bundles on an elliptic surface are changed under logarithmic transformations.
We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…
We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to determine when the moduli space of a stack is a scheme. As an…
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
We introduce and study the Chern filtration on the cohomology of the moduli of bundles on curves. This can be viewed as a natural cohomological invariant defined via tautological classes that interpolates between additive Betti numbers and…
We suggest an effective procedure to calculate numerical invariants for rank two bundles over blown-up surfaces. We study the moduli spaces M_j of bundles on the blown-up plane splitting over the exceptional divisor as O(j)+O(-j). We use…
We prove asymptotic estimates for the volume of families of Orlicz balls in high dimensions. As an application, we describe a large family of Orlicz balls which verify a famous conjecture of Kannan, Lov{\'a}sz and Simonovits about spectral…
We study the unirationality of surface conic bundles $\pi\colon S\to\mathbb P^1$ over an arbitrary field $k$ with discriminant degree $d_S=8$, the first case beyond the del Pezzo range. We divide these surfaces in four families and produce…
Let $(X, H)$ be a polarized smooth projective algebraic surface and $E$ is globally generated, stable vector bundle on $X$. Then the Syzygy bundle $M_E$ associated to it is defined as the kernel bundle corresponding to the evaluation map.…
We study the moduli space $\fM^s(6;3,6,4)$ of simple rank 6 vector bundles $\E$ on $\PP^3$ with Chern polynomial $1+3t+6t^2+4t^3$ and properties of these bundles, especially we prove some partial results concerning their stability. We first…
A conjecture of Batyrev and Manin predicts the asymptotic behaviour of rational points of bounded height on smooth projective varieties over number fields. We prove some new cases of this conjecture for conic bundle surfaces equipped with…
The aim of this paper is to give some characterizations for N-Legendre and N-slant curves in the unit tangent bundles of surfaces endowed with natural diagonal lifted structures.
We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree.
In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological…
In this paper we investigate the asymptotic growth of the number of irreducible and connected components of the moduli space of surfaces of general type corresponding to certain families of surfaces isogenous to a higher product with group…
In this paper we shall generalize the chamber structure of polarizations defined by Qin, and as an application we shall compute the Picard groups of moduli spaces of stable sheaves on a non-rational ruled surface.
We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle…
The aim of this paper is to study some modular contractions of the moduli space of stable pointed curves. These new moduli spaces, which are modular compactifications of the moduli space of smooth pointed curves, are related with the…