10 citations · 55 across the 14 of their papers we have counts for
10 papers · 1 filter
Spectrum of singularities, analytic torsion and Calabi--Yau degenerations
Dennis Eriksson, Gerard Freixas i Montplet
We relate the spectrum of singularities to the geometry of degenerating Calabi--Yau manifolds through holomorphic analytic torsion. We express the leading asymptotic coefficients o…
The Deligne-Riemann-Roch isomorphism
Dennis Eriksson, Gerard Freixas i Montplet
This work establishes the geometric component of Deligne's longstanding program on refined Grothendieck-Riemann-Roch formulas expressed through determinants of cohomology. The appr…
The spectral genus of an isolated hypersurface singularity and a conjecture relating to the Milnor number
Dennis Eriksson, Gerard Freixas i Montplet
In this paper, we introduce the notion of spectral genus of a germ of an isolated hypersurface singularity , defined…
Deligne-Riemann-Roch and intersection bundles
Dennis Eriksson, Gerard Freixas i Montplet
This article is part of a series of works by the authors with the goal of completing a far-reaching program propounded by Deligne, aiming to extend the codimension one part of the…
Complex Chern--Simons bundles in the relative setting
Dennis Eriksson, Gerard Freixas i Montplet, Richard A. Wentworth
Complex Chern-Simons bundles are line bundles with connection, originating in the study of quantization of moduli spaces of flat connections with complex gauge groups. In this pape…
On genus one mirror symmetry in higher dimensions and the BCOV conjectures
Gerard Freixas I Montplet, Dennis Eriksson, Christophe Mourougane
The mathematical physicists Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed, in a seminal article from '94, a conjecture extending genus zero mirror symmetry to higher genera. With…
BCOV invariants of Calabi--Yau manifolds and degenerations of Hodge structures
Dennis Eriksson, Gerard Freixas i Montplet, Christophe Mourougane
Calabi--Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky--Cecotti--Ooguri--Vafa (BCOV), i…
Singularities of metrics on Hodge bundles and their topological invariants
Dennis Eriksson, Gerard Freixas i Montplet, Christophe Mourougane
We consider degenerations of complex projective Calabi--Yau varieties and study the singularities of , Quillen and BCOV metrics on Hodge and determinant bundles. The dominant…
The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms
José Ignacio Burgos Gil, Gerard Freixas i Montplet, Razvan Litcanu
The classical arithmetic Grothendieck-Riemann-Roch theorem can be applied only to projective morphisms that are smooth over the complex numbers. In this paper we generalize the ari…
Hermitian structures on the derived category of coherent sheaves
José Ignacio Burgos Gil, Gerard Freixas i Montplet, Razvan Litcanu
The main objective of the present paper is to set up the theoretical basis and the language needed to deal with the problem of direct images of hermitian vector bundles for project…