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Charton, Isabelle ORCID: 0000-0002-6940-2505 (2020). Hamiltonian S-1-spaces with large equivariant pseudo-index. J. Geom. Phys., 147. AMSTERDAM: ELSEVIER. ISSN 1879-1662

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Abstract

Let (M, omega) be a compact symplectic manifold of dimension 2n endowed with a Hamiltonian circle action with only isolated fixed points. Whenever M admits a toric 1-skeleton S. which is a special collection of embedded 2-spheres in M, we define the notion of equivariant pseudo-index of s: this is the minimum of the evaluation of the first Chern class c(1) on the spheres of S. This can be seen as the analog in this category of the notion of pseudo-index for complex Fano varieties. In this paper we provide upper bounds for the equivariant pseudo-index. In particular, when the even Betti numbers of M are unimodal, we prove that it is at most n + 1. Moreover, when it is exactly n + 1. M must be homotopically equivalent to CPn. (C) 2019 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Charton, Isabelle UNSPECIFIED orcid.org/0000-0002-6940-2505 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-352688
DOI:	10.1016/j.geomphys.2019.103521
Journal or Publication Title:	J. Geom. Phys.
Volume:	147
Date:	2020
Publisher:	ELSEVIER
Place of Publication:	AMSTERDAM
ISSN:	1879-1662
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/35268