Search results for " Geometry."

Hodge Numbers for the Cohomology of Calabi-Yau Type Local Systems

2014

We determine the Hodge numbers of the cohomology group \(H_{L^{2}}^{1}(S, \mathbb{V}) = H^{1}(\bar{S},j_{{\ast}}\mathbb{V})\) using Higgs cohomology, where the local system \(\mathbb{V}\) is induced by a family of Calabi-Yau threefolds over a smooth, quasi-projective curve S. This generalizes previous work to the case of quasi-unipotent, but not necessarily unipotent, local monodromies at infinity. We give applications to Rohde’s families of Calabi-Yau 3-folds.

Pieri’s 1900 Point-and-Motion Memoir

2021

This chapter contains an English translation of Mario Pieri’s 1900a memoir, On Elementary Geometry as a Hypothetical Deductive System: Monograph on Point and on Motion.1 By elementary geometry, Pieri meant Euclidean geometry as taught then in elementary courses, except for the theorems dependent on the Euclidean parallel axiom.

Zur Geometrie der Translationsstrukturen mit eigentlichen Dilatationen

1983

Spectral invariance for algebras of pseudodifferential operators on besov-triebel-lizorkin spaces

1993

The algebra of pseudodifferential operators with symbols inS1,δ0, δ<1, is shown to be a spectrally invariant subalgebra of ℒ(bp,qs) and ℒ(Fp,qs).

Ein Axiomensystem f�r partielle affine R�ume

1994

A partial linear space with parallelism is called partial affine space if it is embeddable in an affine space with the same pointset preserving the parallelism. These partial affine spaces will be characterized by a system of three axioms for partial linear spaces with parallelism.

Generalizations of Clausen's formula and algebraic transformations of Calabi-Yau differential equations

2011

AbstractWe provide certain unusual generalizations of Clausen's and Orr's theorems for solutions of fourth-order and fifth-order generalized hypergeometric equations. As an application, we present several examples of algebraic transformations of Calabi–Yau differential equations.

The polyhedral Hodge number $h^{2,1}$ and vanishing of obstructions

2000

We prove a vanishing theorem for the Hodge number $h^{2,1}$ of projective toric varieties provided by a certain class of polytopes. We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope. In particular, the vanishing theorem for $h^{2,1}$ implies that these deformations are unobstructed.

A class of unitals of order q which can be embedded in two different planes of order q2

1987

By deriving the desarguesian plane of order q2 for every prime power q a unital of order q is constructed which can be embedded in both the Hall plane and the dual of the Hall plane of order q2 which are non-isomorphic projective planes. The representation of translation planes in the fourdimensional projective space of J. Andre and F. Buekenhouts construction of unitals in these planes are used. It is shown that the full automorphism groups of these unitals are just the collineation groups inherited from the classical unitals.

The module structure of Hochschild homology in some examples

2008

Abstract In this Note we give a simple proof of a conjecture by A. Caldararu stating the compatibility between the modified Hochschild–Kostant–Rosenberg isomorphism and the action of Hochschild cohomology on Hochschild homology in the case of Calabi–Yau manifolds and smooth projective curves. To cite this article: E. Macri` et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves

2006

In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can be studied using the technique of matrix problems or via Fourier-Mukai transforms, both methods are discussed here. Moreover, we include new proofs of some classical results about vector bundles on elliptic curves.