Related papers: Eta forms and determinant lines
We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over…
The Quillen-Bismut-Freed construction associates a determinant line bundle with connection to an infinite dimensional super vector bundle with a family of Dirac-type operators. We define the regularized first Chern form of the infinite…
In this article we study the Quillen norm on the determinant line bundle associated with a family of complex curves with cusps, which admit singular fibers. More precisely, we fix a family of complex curves $\pi : X \to S$, which admit at…
We prove two geometric index theorems for a family of first-order elliptic operators over a manifold with boundary by computing eta form representatives for the Chern character classes of the index bundle. The eta forms occur as relative…
It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with…
We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen's original construction for Riemann surfaces and using zeta regularized determinant of Laplacians, one…
In this note we examine the question of expressing the determinant of the push forward of a symmetric line bundle on an abelian fibration in terms of the pull back of the relative dualizing sheaf via the zero section.
We show the existence of a symplectic structure on the moduli space of the Seiberg-Witten equations on $\Sigma \times \Sigma$ where $\Sigma$ is a compact oriented Riemann surface. To prequantize the moduli space, we construct a Quillen-type…
We explain the bundle structures of the {\it Determinant line bundle} and the {\it Quillen determinant line bundle} considered on the connected component of the space of Fredholm operators including the identity operator in an intrinsic…
The Seiberg-Witten family of elliptic curves defines a Jacobian rational elliptic surface $\Z$ over $\mathbb{C}\mathrm{P}^1$. We show that for the $\bar{\partial}$-operator along the fiber the logarithm of the regularized determinant $-1/2…
In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic…
We discuss the $\zeta-$regularized determinant of elliptic boundary value problems on a line segment. Our framework is applicable for separated and non-separated boundary conditions.
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…
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…
In this note we specialize and illustrate the ideas developed in the paper math.DG/0201112 of the first author ("Index theory, eta forms, and Deligne cohomology ") in the case of the determinant line bundle. We discuss the surgery formula…
We investigate the symplectic geometric and differential geometric aspects of the moduli space of connections on a compact Riemann surface $X$. Fix a theta characteristic $K^{1/2}_X$ on $X$; it defines a theta divisor on the moduli space…
In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising from the $L^2$ metric and we construct a prequantum line bundle whose curvature is proportional to this symplectic…
Given a proper, open, holomorphic map of K\"ahler manifolds, whose general fibers are Calabi-Yau manifolds, the volume forms for the Ricci-flat metrics induce a hermitian metric on the relative canonical bundle over the regular locus of the…
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…
By the family index theory, we generalize some well-known $SL(2,Z)$ modular forms to the family case and obtain some new anomaly cancellation formulas for the determinant line bundle and index gerbes, and certain results about eta…