相关论文: Determinant bundle in a family of curves, after A.…

We investigate principal bundles over a root stack. In case of dimension one, we generalize the criterion of Weil and Atiyah for a principal bundle to have an algebraic connection.

Raynaud and Gruson showed that there is a reasonable algebro-geometric notion of family of discrete (infinite-dimensional) vector spaces. The author introduces a notion of family of Tate spaces ("Tate" means "locally linearly compact") and…

This paper is motivated by Deninger's programme. First we prove, using Alvarez Lopez-Kordyukov results, an Atiyah-Bott-Lefschetz trace formula for the cohomology groups associated to a ramified leafwise flat line bundle on a riemannian…

This is a continuation of "Rational families of vector bundles on curves, I". Let C be a smooth projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1.…

For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second Beilinson-Chern class. Applied to the cotangent bundle, this may be regarded as a higher analogue of the canonical line…

Given a projective morphism of compact, complex, algebraic varieties and a relatively ample line bundle on the domain we prove that a suitable choice, dictated by the line bundle, of the decomposition isomorphism of the Decomposition…

This paper is concerned with the study of the geometry of determinant line bundles associated to families of spectral triples parametrized by the moduli space of gauge equivalent classes of Hermitian connections on a Hermitian finite…

For a Riemann surface $X$ and the moduli of regularly stable $G$-bundles $M$, there is a naturally occuring "$adjoint$" vector bundle over $X \times M$. One can take the determinant of this vector bundle with respect to the projection map…

To a symmetric, relatively ample line bundle on an abelian scheme one can associate a linear combination of the determinant bundle and the relative canonical bundle, which is a torsion element in the Picard group of the base. We improve the…

Drawing on work of Berndtsson and of Lempert and Sz\H{o}ke, we define a kind of complex analytic structure for families of (possibly finite-dimensional) Hilbert spaces that might not fit together to form a holomorphic vector bundle but…

We define and study a simplicial complex which is a homogeneous space for the group $PGL(2, K)$ over a two-dimensional local field $K$. The complex is a generalization of the tree studied by F. Bruhat, J. Tits, J.-P. Serre and P. Cartier in…

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$ of rank 2 vector bundles canonically…

Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates…

We translate the Atiyah's results on classification of vector bundles on elliptic curves to the language of factors of automorphy.

A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…

We compute the algebraic equation of the universal family over the Kenyon-Smillie $(2,3,4)$-Teichm\"uller curve and give a nice geometric description of the torsion map. Moreover, we re-prove independently that the found algebraic equation…

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define…

The higher direct image complex of a coherent sheaf (or finite complex of coherent sheaves) under a projective morphism is a fundamental construction that can be defined via a Cech complex or an injective resolution, both inherently…

We consider the assembly map for principal bundles with fiber a countable discrete group. We obtain an index-theoretic interpretation of this homomorphism by providing a tensor-product presentation for the module of sections associated to…

For the first obstruction to extending a holomorphic vector bundle from a submanifold of a complex manifold found by Griffiths we give an explicit formula in terms of the Atiyah class of the bundle.