Related papers: Vector Bundles over Elliptic Fibrations

We study function theory and K\"ahler geometry on total spaces of vector bundles on an elliptic curve. For rank two vector bundles of degree zero, we show that any two total spaces are biholomorphic if and only if the corresponding vector…

We give a method to construct deep holes for elliptic curve codes. For long elliptic curve codes, we conjecture that our construction is complete in the sense that it gives all deep holes. Some evidence and heuristics on the completeness…

We construct a natural generalized complex structure on the total space of any bundle endowed with a Chern connection and whose typical fibre is a homogeneous symplectic manifold. This extends known constructions of generalized complex…

We give conditions ensuring that a neighborhood of an embedded projective space bundle over an elliptic curve is holomorphically equivalent to a neighborhood of the zero section of its normal bundle.

We study vector bundles on curves with rational tails and their smoothings and give a sufficient condition for the general fibre to be balanced.

Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple…

We study topologically trivial $G$-Higgs bundles over an elliptic curve $X$ when the structure group $G$ is a connected real form of a complex semisimple Lie group $G^{\mathbb{C}}$. We achieve a description of their (reduced) moduli space,…

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^*$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.

A constructive method is given for obtaining cospectral vertices in undirected graphs, along with an operation that preserves this construction. We prove that the construction yields cospectral vertices, as well as strongly cospectral…

This thesis examines the relationship between elliptic curves with complex multiplication and Lambda structures. Our main result is to show that the moduli stack of elliptic curves with complex multiplication, and the universal elliptic…

In this survey article, we summarise the known results towards the conjecture: elliptic curves over totally real number fields are modular. For understanding these recent results in the literature, we present some necessary background along…

We present a geometric model for the category of vector bundles over the weighted projective line of type (2,2,n). This model is based on the orbit space of an infinite marked strip under a specific group action. We establish a bijection…

We introduce and motivate a conjecture about the existence of complete, 1-dimensional families of covers of an elliptic curve. If the conjecture holds, then it would imply a uniform lower bound of 5 for slope of the moduli space of curves.…

Nous presentons diverses applications des fibres vectoriels aux equations aux q-differences, dans la lignee de la correspondance de Weil. (We present some applications of vector bundles to $q$-difference equtions, in continuation of Weil's…

This paper focuses on the study of a new category of vector bundles. The objects of this category, called chiral vector bundles, are pairs given by a complex vector bundle along with one of its automorphisms. We provide a classification for…

We generalize Horrocks' criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension at least four, over…

Extending a previous result of the authors, we classify globally generated vector bundles on projective spaces with first Chern class equal to three.

In this paper, we present several methods for construction of elliptic curves with large torsion group and positive rank over number fields of small degree. We also discuss potential applications of such curves in the elliptic curve…

We investigate the analytic classification of two dimensional neighborhoods of an elliptic curve with torsion normal bundle. We provide the complete analytic classification for those neighborhoods in the simplest formal class and we…