Generalized holomorphic analytic torsion

Burgos Gil, José Ignacio, Freixas i Montplet, Gerard, and Liţcanu, Răzvan. "Generalized holomorphic analytic torsion." Journal of the European Mathematical Society 016.3 (2014): 463-535. <http://eudml.org/doc/277405>.

@article{BurgosGil2014,
abstract = {In this paper we extend the holomorphic analytic torsion classes of Bismut and Köhler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the theories of generalized holomorphic analytic torsion classes for projective morphisms. The extension of the holomorphic analytic torsion classes of Bismut and Köhler is obtained as the theory of generalized analytic torsion classes associated to $–R=2$, $R$ being the $R$-genus. As an application of the axiomatic characterization, we give new simpler proofs of known properties of holomorpic analytic torsion classes, we give a characterization of the $R$-genus, and we construct a direct image of hermitian structures for projective morphisms.},
author = {Burgos Gil, José Ignacio, Freixas i Montplet, Gerard, Liţcanu, Răzvan},
journal = {Journal of the European Mathematical Society},
keywords = {Grothendieck–Riemann–Roch theorem; holomorphic analytic torsion; Quillen metric; Grothendieck duality; Grothendieck-Riemann-Roch theorem; holomorphic analytic torsion; Quillen metric; Grothendieck duality},
language = {eng},
number = {3},
pages = {463-535},
publisher = {European Mathematical Society Publishing House},
title = {Generalized holomorphic analytic torsion},
url = {http://eudml.org/doc/277405},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Burgos Gil, José Ignacio
AU - Freixas i Montplet, Gerard
AU - Liţcanu, Răzvan
TI - Generalized holomorphic analytic torsion
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 3
SP - 463
EP - 535
AB - In this paper we extend the holomorphic analytic torsion classes of Bismut and Köhler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the theories of generalized holomorphic analytic torsion classes for projective morphisms. The extension of the holomorphic analytic torsion classes of Bismut and Köhler is obtained as the theory of generalized analytic torsion classes associated to $–R=2$, $R$ being the $R$-genus. As an application of the axiomatic characterization, we give new simpler proofs of known properties of holomorpic analytic torsion classes, we give a characterization of the $R$-genus, and we construct a direct image of hermitian structures for projective morphisms.
LA - eng
KW - Grothendieck–Riemann–Roch theorem; holomorphic analytic torsion; Quillen metric; Grothendieck duality; Grothendieck-Riemann-Roch theorem; holomorphic analytic torsion; Quillen metric; Grothendieck duality
UR - http://eudml.org/doc/277405
ER -