Related papers: On two open questions for extension bundles

Multiplicative bundle gerbes are gerbes over a Lie group which are compatible with the group structure. In this article connections on such bundle gerbes are introduced and studied. It is shown that multiplicative bundle gerbes with…

We present a geometric interpretation of tight closure in terms of vector bundles and projective bundles.

Let $X$ be a projective nonsingular toric 3-fold with a surjective torus equivariant morphism onto the projective line. Then we prove that an ample line bundle on $X$ is always normally generated.

Let $X$ be a projective variety over a field. In this paper, we will construct a moduli space of very ample line bundles on $X$. In doing so, we develop a generalization of Fitting ideals to complexes of sheaves on $X$. We give other…

This paper has two goals. The first is to present the construction, due to the author, of measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications. We take this opportunity to add…

We establish a striking connection between Abramovich's and Vistoli's twisted bundles and Gieseker vector bundles. This note grew out of an attempt to understand a recent draft of Seshadri.

We study deformation theory of elliptic fibre bundles over curves in positive characteristics. As applications, we give examples of non-liftable elliptic surfaces in charactertic two and three, which answers a question of Katsura and Ueno.…

Exceptional sequences of line bundles on a smooth projective toric surface are automatically full when they can be constructed via augmentation. By using spherical twists, we give examples that there are also exceptional sequences which can…

I introduce new Langlands duality conjectures concerning skein modules of 3-manifolds, which we have made recently with David Ben-Zvi, Sam Gunningham, and Pavel Safronov. I recount some historical motivation and some recent special cases…

We provide a new characterisation of the decades old open problem of extending bilipschitz mappings given on a Euclidean separated net. In particular, this allows for the complete positive solution of the open problem in dimension two.…

We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of…

The aim of this work is to construct examples of pairs whose logarithmic cotangent bundles have strong positivity properties. These examples are constructed from any smooth n-dimensional complex projective varieties by considering the sum…

Let $X$ be a compact K\"ahler manifold. We extend the notion of Quillen metric to the set of integrable line bundles on $X$. In particular, we prove that the notion of holomorphic analytic torsion extends to integrable line bundles…

Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…

Let $P(E)$ be the projectivization of a holomorphic vector bundle $E$ over a compact complex curve $C$. We characterize the existence of an extremal K\"ahler metric on the ruled manifold $P(E)$ in terms of relative K-polystability and the…

We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions…

Results in the preliminary version have been strengthed. In addition, Batyrev's conjectural formula for quantum cohomology of projective bundles associated to direct sum of line bundles over $\Pee^n$ is partially verified.

In this article we describe vector bundles over projectivoid line and show how it is similar to (and different) from Gorthendieck's classification of vector bundles over projective line.

We study complex compact Kaehler manifolds $X$ carrying a contact structure. If $X$ is almost homogeneous and $b_2(X) \geq 2$, then $X$ is a projectivised tangent bundle (this was known in the projective case even without assumption on the…

The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in…