# Generalized holomorphic analytic torsion

José Ignacio Burgos Gil; Gerard Freixas i Montplet; Răzvan Liţcanu

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 3, page 463-535
- ISSN: 1435-9855

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topBurgos 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 -

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