Related papers: Variation of the holomorphic determinant bundle

This work establishes the geometric component of Deligne's longstanding program on refined Grothendieck-Riemann-Roch formulas expressed through determinants of cohomology. The approach relies on a newly developed universal category of Chern…

The goal of this paper is to prove Riemann-Roch type theorems for Deligne-Mumford algebraic stacks. To this end, we introduce a "cohomology with coefficients in representations" and a Chern character, and we prove a…

This article deals with two topics: the first, which has a general character, is a variation formula for the the determinant line bundle in non-K\"ahlerian geometry. This formula, which is a consequence of the non-K\"ahlerian version of the…

Given a Liouville manifold, we compute a Floer-homotopical invariant -- the complexification of the lift of symplectic cohomology to complex cobordism -- in terms of a classical Floer-theoretic invariant, namely, symplectic cohomology…

In this paper we give a criterion for a deformation of a hermitian vector bundle to be Ricci-flat. As an application we show that on a K\"ahler manifold, every deformation of a vector bundle can be made Ricci-flat whereas on some Hopf…

We compute the moduli of endomorphisms of the de Rham and crystalline cohomology functors, viewed as a cohomology theory on smooth schemes over truncated Witt vectors. As applications of our result, we deduce Drinfeld's refinement of the…

In this paper, we give a combinatorial formula for the \v{C}ech cocycles representing the power sums of the Chern roots of a holomorphic vector bundle over a complex manifold. By an observation motivation by author's previous paper, we also…

In this paper, we prove the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level.

Given a holomorphic Hermitian vector bundle and a star-product with separation of variables on a pseudo-Kaehler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle which also has the…

Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic $L^2$ torsion, which lies in the determinant line of the twisted $L^2$ Dolbeault cohomology and represents a volume element there.…

Grothendieck has proved that each class in the de Rham cohomology of a smooth complex affine variety can be represented by a differential form with polynomial coefficients. After having proved a single exponential bound for the degrees of…

A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X,L), the cohomologies of L over the GIT quotient X // G equal the invariant part of…

Let $X$ be a smooth projective variety acted on by a reductive group $G$. Let $L$ be a positive $G$-equivariant line bundle over $X$. We use the Witten deformation of the Dolbeault complex of $L$ to show, that the cohomology of the sheaf of…

We prove that invariant subbundles of the Kontsevich-Zorich cocycle respect the Hodge structure. In particular, we establish a version of Deligne semisimplicity in this context. This implies that invariant subbundles must vary polynomially…

As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near…

We consider smooth vector bundles over smooth manifolds equipped with non-smooth geometric data. For nilpotent differential operators acting on these bundles, we show that the kernels of induced Hodge-Dirac-type operators remain isomorphic…

In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of…

We produce an equality between the Gromov-Witten invariants of the moduli space M of rank two odd degree stable vector bundles over a Riemann surface $\Sigma$ and the Donaldson invariants of the algebraic surface $\Sigma \times P^1$. We…

Link invariants, for 3-manifolds, are defined in the context of the Rozansky-Witten theory. To each knot in the link one associates a holomorphic bundle over a holomorphic symplectic manifold X. The invariants are evaluated for b_{1}(M)…

We show that any compact Kahler manifold with integral Kahler form, parametrizes a natural holomorphic family of Cauchy-Riemann operators on the Riemann sphere such that the Quillen determinant line bundle of this family is isomorphic to a…