Related papers: Formulae for Line Bundle Cohomology on Calabi-Yau …
We conjecture and prove closed-form index expressions for the cohomology dimensions of line bundles on del Pezzo and Hirzebruch surfaces. Further, for all compact toric surfaces we provide a simple algorithm which allows expression of any…
We analyse line bundle cohomologies on all favourable co-dimension two Complete Intersection Calabi Yau (CICY) manifolds of Picard number two. Our results provide further evidence that the cohomology dimensions of such line bundles are…
We determine several classes of smooth complex projective surfaces on which Zariski decomposition can be combined with vanishing theorems to yield cohomology formulae for all line bundles. The obtained formulae express cohomologies in terms…
Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued…
We give the first numerical calculation of the spectrum of the Laplacian acting on bundle-valued forms on a Calabi-Yau three-fold. Specifically, we show how to compute the approximate eigenvalues and eigenmodes of the Dolbeault Laplacian…
This paper explores the possibility of constructing multivariate generating functions for all cohomology dimensions of all holomorphic line bundles on certain complex projective varieties of Fano, Calabi-Yau and general type in various…
We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds…
Let $X$ be a smooth projective Calabi-Yau variety and $L$ a Koszul line bundle on $X$. We show that for Betti numbers of a maximal Cohen-Macaulay module over the homogeneous coordinate ring $A$ of $X$ there are formulas similar to the…
This thesis contributes with a number of topics to the subject of string compactifications. In the first half of the work, I discuss the Hodge plot of Calabi-Yau threefolds realised as hypersurfaces in toric varieties. The intricate…
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…
We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, we construct positive rank five monad bundles over…
Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the…
We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these…
We extend the previous computations of Hermitian Yang-Mills connections for bundles on complete intersection Calabi-Yau manifolds to bundles on their free quotients. Bundles on quotient manifolds are often defined by equivariant bundles on…
Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional…
We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.
The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative…
We describe the package "IncidenceCorrespondenceCohomology" for the computer algebra system Macaulay2. The main feature concerns the computation of characters and dimensions for the cohomology groups of line bundles on the incidence…
Based on the method by [K\"uc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles on Grassmannians for each dimension. In particular, we…
The aim of this paper is to classify indecomposable rank 2 arithmetically Cohen-Macaulay (ACM) bundles on compete intersection Calabi-Yau (CICY) threefolds and prove the existence of some of them. New geometric properties of the curves…