## Canonical holomorphic sections of determinant line bundles

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

#### Standard

Canonical holomorphic sections of determinant line bundles. / Kaad, Jens; Nest, Ryszard.

I: Journal fur die Reine und Angewandte Mathematik, Bind 746, 2019, s. 67-116.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

#### Harvard

Kaad, J & Nest, R 2019, 'Canonical holomorphic sections of determinant line bundles', Journal fur die Reine und Angewandte Mathematik, bind 746, s. 67-116. https://doi.org/10.1515/crelle-2015-0114

#### APA

Kaad, J., & Nest, R. (2019). Canonical holomorphic sections of determinant line bundles. Journal fur die Reine und Angewandte Mathematik, 746, 67-116. https://doi.org/10.1515/crelle-2015-0114

#### Vancouver

Kaad J, Nest R. Canonical holomorphic sections of determinant line bundles. Journal fur die Reine und Angewandte Mathematik. 2019;746:67-116. https://doi.org/10.1515/crelle-2015-0114

#### Author

Kaad, Jens ; Nest, Ryszard. / Canonical holomorphic sections of determinant line bundles. I: Journal fur die Reine und Angewandte Mathematik. 2019 ; Bind 746. s. 67-116.

#### Bibtex

@article{d956c70ccab649bebb95c4368cca52ea,
title = "Canonical holomorphic sections of determinant line bundles",
abstract = "We investigate the analytic properties of torsion isomorphisms (determinants) of mapping cone triangles of Fredholm complexes. Our main tool is a generalization to Fredholm complexes of the perturbation isomorphisms constructed by R. Carey and J. Pincus for Fredholm operators. A perturbation isomorphism is a canonical isomorphism of determinants of homology groups associated to a finite rank perturbation of Fredholm complexes. The perturbation isomorphisms allow us to establish the invariance properties of the torsion isomorphisms under finite rank perturbations. We then show that the perturbation isomorphisms provide a holomorphic structure on the determinant lines over the space of Fredholm complexes. Finally, we establish that the torsion isomorphisms and the perturbation isomorphisms provide holomorphic sections of certain determinant line bundles.",
author = "Jens Kaad and Ryszard Nest",
year = "2019",
doi = "10.1515/crelle-2015-0114",
language = "English",
volume = "746",
pages = "67--116",
journal = "Journal fuer die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walterde Gruyter GmbH",

}

#### RIS

TY - JOUR

T1 - Canonical holomorphic sections of determinant line bundles

AU - Nest, Ryszard

PY - 2019

Y1 - 2019

N2 - We investigate the analytic properties of torsion isomorphisms (determinants) of mapping cone triangles of Fredholm complexes. Our main tool is a generalization to Fredholm complexes of the perturbation isomorphisms constructed by R. Carey and J. Pincus for Fredholm operators. A perturbation isomorphism is a canonical isomorphism of determinants of homology groups associated to a finite rank perturbation of Fredholm complexes. The perturbation isomorphisms allow us to establish the invariance properties of the torsion isomorphisms under finite rank perturbations. We then show that the perturbation isomorphisms provide a holomorphic structure on the determinant lines over the space of Fredholm complexes. Finally, we establish that the torsion isomorphisms and the perturbation isomorphisms provide holomorphic sections of certain determinant line bundles.

AB - We investigate the analytic properties of torsion isomorphisms (determinants) of mapping cone triangles of Fredholm complexes. Our main tool is a generalization to Fredholm complexes of the perturbation isomorphisms constructed by R. Carey and J. Pincus for Fredholm operators. A perturbation isomorphism is a canonical isomorphism of determinants of homology groups associated to a finite rank perturbation of Fredholm complexes. The perturbation isomorphisms allow us to establish the invariance properties of the torsion isomorphisms under finite rank perturbations. We then show that the perturbation isomorphisms provide a holomorphic structure on the determinant lines over the space of Fredholm complexes. Finally, we establish that the torsion isomorphisms and the perturbation isomorphisms provide holomorphic sections of certain determinant line bundles.

U2 - 10.1515/crelle-2015-0114

DO - 10.1515/crelle-2015-0114

M3 - Journal article

VL - 746

SP - 67

EP - 116

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

ER -

ID: 212506589