Universität zu Köln

Godinho, Leonor, Lindsay, Nicholas and Sabatini, Silvia ORCID: 0000-0001-7521-321X (2025). On a symplectic generalization of a Hirzebruch problem. Journal of Fixed Point Theory and Applications, 27 (3). pp. 1-73. Springer Nature. ISSN 1661-7738

PDF s11784-025-01224-0.pdf Bereitstellung unter der CC-Lizenz: Creative Commons Attribution. Download (2MB)

Abstract

[Artikel-Nr. 75] Motivated by a problem of Hirzebruch, we study 8-dimensional, closed, connected, symplectic manifolds having a Hamiltonian torus ac- tion with isolated fixed points and second Betti number equal to 1. Such manifolds are automatically positive monotone. Our main result concerns those endowed with a Hamiltonian T 2-action and fourth Betti number equal to 2. We classify their isotropy data, (equivariant) co- homology rings and (equivariant) Chern classes, and prove that they agree with those of certain explicit Fano 4-folds with torus actions. We apply our results to obtain new consequences for Hirzebruch’s problem in the algebraic setting. Moreover, under more general assumptions, we prove several finiteness results concerning Betti and Chern numbers of 8-dimensional, positive monotone symplectic manifolds with a Hamil- tonian torus action.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Godinho, Leonor UNSPECIFIED UNSPECIFIED UNSPECIFIED Lindsay, Nicholas UNSPECIFIED UNSPECIFIED UNSPECIFIED Sabatini, Silvia UNSPECIFIED https://orcid.org/0000-0001-7521-321X UNSPECIFIED
URN:	urn:nbn:de:hbz:38-805034
Identification Number:	10.1007/s11784-025-01224-0
Journal or Publication Title:	Journal of Fixed Point Theory and Applications
Volume:	27
Number:	3
Page Range:	pp. 1-73
Number of Pages:	73
Date:	1 September 2025
Publisher:	Springer Nature
ISSN:	1661-7738
Language:	English
Faculty:	Faculty of Medicine
Divisions:	Zentrum für Molekulare Medizin
Subjects:	Medical sciences Medicine
Uncontrolled Keywords:	Keywords Language Positive monotone symplectic manifolds ; Fano 4-folds ; Hirzebruch problem number 27 English
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/80503