Related papers: On the computation of intersection numbers for twi…

The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…

This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…

We introduce the concept of braided alternative bialgebra. The theory of cocycle bicrossproducts for alternative bialgebras is developed. As an application, the extending problem for alternative bialgebra is solved by using some non-abelian…

We give several algorithms addressing computations of intersections of conjugate subgroups.

We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…

We consider the Quot scheme, R_{d}, compactifying the space of degree d maps from the projective line to the Grassmannian of lines. We give an algorithm for computing the degree of R_{d} under a "generalized Pl\"ucker embedding", this is a…

Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…

This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second…

For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic…

This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed the Shimura curve over Q associated to a…

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and…

Introduction of curvilinear coordinates might be very convenient in many cases. Theoretically, tensor analysis would be most suited. However, tensor notation can't be used in numerical procedure. For example, the strict discrimination of…

A likelihood function on a smooth very affine variety gives rise to a twisted de Rham complex. We show how its top cohomology vector space degenerates to the coordinate ring of the critical points defined by the likelihood equations. We…

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…

We calculate the cohomology spaces of the Hilbert schemes of points on surfaces with values in locally constant systems. For that purpose, we generalise I. Grojnoswki's and H. Nakajima's description of the ordinary cohomology in terms of a…

We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as…

In this paper we outline an algorithmic approach to compute Puiseux series expansions for algebraic surfaces. The series expansions originate at the intersection of the surface with as many coordinate planes as the dimension of the surface.…

We consider the Alexander polynomial of a plane algebraic curve twisted by a linear representation. We show that it divides the product of the polynomials of the singularity links, for unitary representations. Moreover, their quotient is…

We give a recipe to compute the geometric intersection number of an integral lamination with a particular type of integral lamination on an n-times punctured disk. This provides a way to find the geometric intersection number of two…

Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection…