Related papers: Surface Bundles With Non-Zero Signature

This paper explores the cohomological consequences of the existence of moduli spaces for flat bundles with bounded rank and irregularity at infinity and gives unconditional proofs. Namely, we prove the existence of a universal bound for the…

This work provides a curve-based approach to Ulrich bundles on surfaces, establishing a correspondence that characterizes their existence, with a focus on applications to surfaces in $\mathbb{P}^3$.

Different techniques from machine learning are applied to the problem of computing line bundle cohomologies of (hypersurfaces in) toric varieties. While a naive approach of training a neural network to reproduce the cohomologies fails in…

An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which…

A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…

We present a proposal for an undeniable signature scheme based in supersingular hyperelliptic curves of genus 2.

A definition of non-abelian genus zero open Wilson surfaces is proposed. The ambiguity in surface-ordering is compensated by the gauge transformations.

Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes…

We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…

In this paper we give the classification of rank 3 vector bundles without "inner" cohomology on a quadric hypersurface \Q_n (n>3) by studying the associated monads.

The aim of this paper is to establish an equivalence of certain categories of Higgs bundles on a non-isotrivial elliptic surface $\pi: X \rightarrow C$ with $\chi(X) > 0$ and certain categories of Parabolic Higgs bundles on $C$

We prove that a continuous path with finite length in a real Banach space cannot have infinitely many zero components in its signature unless it is tree-like. In particular, this allows us to strengthen a limit theorem for signature…

Let $A$ be an abelian scheme of dimension at least four over a $\mathbb{Z}$-finitely generated integral domain $R$ of characteristic zero, and let $L$ be an ample line bundle on $A$. We prove that the set of smooth hypersurfaces $D$ in $A$…

This short paper shows that a projective bundle over a smooth variety with a section can be uniquely recovered from the embedding of the section in its second infinitesimal neighborhood within the bundle.

We demonstrate that stacking topologically trivial layers, under enforced symmetry restrictions, yields emergent topological phases with protected boundary states. Remarkably, the number of layers itself acts as a topological switch,…

In this paper, we begin an investigation of infinite genus handlebodies, infinitely generated Schottky groups, and related uniformization questions by giving appropriate definitions for them. There are uncountably many topological types of…

The construction for nonreduced projective moduli scheme of semistable admissible pairs is performed. We establish the relation of this moduli scheme with reduced moduli scheme built up in the previous article and prove that nonreduced…

We show that a compact complex surface which fibers smoothly over a curve of genus >1 with fibers of genus >1 fibers holomorphically. We deduce an improvement of a result in [D Kotschick, Math. Research Letters, 5 (1998) 227-234], and a…

We prove effective upper bounds on the global sections of nef line bundles of small generic degree over a fibered surface over a field of any characteristic. It can be viewed as a relative version of the classical Noether inequality for…

We use bounds of character sums and some combinatorial arguments to show the abundance of very smooth numbers which also have very few non-zero binary digits.