Related papers: Bundles computing Clifford indices on trigonal cur…

Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left…

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 $\mathbb{P}^3$.

In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…

Given a unipotent bundle of smooth manifolds we construct its secondary transfer map and show that this map determines the higher smooth torsion of the bundle. This approach to higher torsion provides a new perspective on some of its…

In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra $C_f$ of a ternary cubic form $f$ and certain vector bundles (called Ulrich bundles) on a cubic surface $X$.…

For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on…

Clifford theory of possibly infinite dimensional modules is studied

In this paper we investigate line bundles on $\mathrm{Bun}_{\mathcal{G}}$ the moduli stack of parahoric Bruhat--Tits bundles over a smooth projective curve. Translating this problem into one concerning twisted conformal blocks, we are able…

Given a curve over a finite field, we compute the number of stable bundles of not necessarily coprime rank and degree over it. We apply this result to compute the virtual Poincare polynomials of the moduli spaces of stable bundles over a…

Starting from a general analysis of obstruction classes, we develop the investigation of obstructions associated with the bundle structure of the hyperbolic Clifford algebra. By taking into account particularities arising from the Whitney…

We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of…

In this paper we study higher Gaussian (or Wahl) maps for the canonical bundle of certain smooth projective curves. More precisely, we determine the rank of higher Gaussian maps of the canonical bundle for plane curves, for curves contained…

CLIFFORD performs various computations in Grassmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in Cl(B) - the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B.…

The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.

Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G-bundles on any smooth projective curve over k.

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social…

We propose a conjecture on the generating series of Chern numbers of tautological bundles on Hilbert schemes of points on curves and establish the rank 1 and rank -1 case of this conjecture. Thus we compute explicitly the generating series…

Computing the topology of an algebraic plane curve $\mathcal{C}$ means to compute a combinatorial graph that is isotopic to $\mathcal{C}$ and thus represents its topology in $\mathbb{R}^2$. We prove that, for a polynomial of degree $n$ with…

We introduce the Non-commutative Subset Convolution - a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of…

Clustering coefficient is one of the most useful indices in complex networks. However, graph theoretic properties of this metric have not been discussed much in the literature, especially in graphs resulting from some binary operations. In…