Related papers: Surface Bundles With Non-Zero Signature

We construct examples of non-isotrivial algebraic families of smooth complex projective curves over a curve of genus 2. This solves a problem from Kirby's list of problems in low-dimensional topology. Namely, we show that 2 is the smallest…

Given a complex projective surface with an ADE singularity and p_{g}=0, we construct ADE bundles over it and its minimal resolution. Furthermore, we descibe their minuscule representation bundles in terms of configurations of (reducible)…

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of…

We give an upper bound for the number of points of a hypersurface over a finite field that has no lines on, in terms of the dimension, the degree, and the number of the elements of the finite field.

In this article, we investigate the stability of syzygy bundles corresponding to ample and globally generated vector bundles on smooth irreducible projective surfaces.

We produce an example of a rigid, but not infinitesimally rigid smooth compact complex surface with ample canonical bundle using results about arrangements of lines inspired by work of Hirzebruch, Kapovich and Millson, Manetti and Vakil.

A new $(1,1)$-dimensional super vector bundle which exists on any super Riemann surface is described. Cross-sections of this bundle provide a new class of fields on a super Riemann surface which closely resemble holomorphic functions on a…

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 construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of…

A surface with boundary is randomly generated by gluing polygons along some of their sides. We show that its genus and number of boundary components asymptotically follow a bivariate normal distribution.

We construct exceptional sequences of line bundles of maximal length on a family of surfaces isogenous to a higher product of unmixed type with $p_g=q=0$.

We establish the existence of models of quadric surface bundles with prescribed \'etale local forms.

We construct an infinite family of homologous, non-isotopic, symplectic surfaces of any genus greater than one in a certain class of closed, simply connected, symplectic four-manifolds. Our construction is the first example of this…

In this article we give several examples of line bundles on certain non-compact surfaces that cannot be equipped with a flat connection.

We show that the anti-canonical bundle of any $\mathbb Q$-factorial surface is numerically effective if and only if it is pseudo-effective. To prove this, we establish a numerical non-vanishing theorem for surfaces polarized with…

Surfaces of general type with positive second Segre number are known to have big cotangent bundle. We give a new criterion ensuring that a surface of general type with canonical singularities has a minimal resolution with big cotangent…

In some of object recognition problems, labeled data may not be available for all categories. Zero-shot learning utilizes auxiliary information (also called signatures) describing each category in order to find a classifier that can…

We develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.

We give the new effective criterion for the global generation of the adjoint bundle on normal surfaces with a boundary. We could make the invariant \delta small a bit more on log-terminal singular point, and then we could prove the theorem…