Holomorphic one-forms, fibrations over the circle, and characteristic numbers of Kähler manifolds

Kotschick, D. (2022): Holomorphic one-forms, fibrations over the circle, and characteristic numbers of Kähler manifolds. In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 172, No. 1: pp. 95-103

Abstract

We prove that the only relation imposed on the Hodge and Chern numbers of a compact Kähler manifold by the existence of a nowhere zero holomorphic one-form is the vanishing of the Hirzebruch genus. We also treat the analogous problem for nowhere zero closed one-forms on smooth manifolds.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0305-0041
• Language: English