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On the Zeroes of Meromorphic Vector-Fields

In: Essays on Topology and Related Topics

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  • Paul F. Baum
  • Raoul Bott

Abstract

Let M be a compact complex analytic manifold and let x be a holomorphic vector-field on M. In an earlier paper by one of us (see [2]) it was shown that the behavior of x near its zeroes determined all the Chern numbers of M and the nature of this determination was explicitly given where x had only nondegenerate zeroes. The primary purpose of this note is to extend this result to meromorphic fields, or equivalently to sections s of T⊗L where T is the holomorphic tangent bundle to M and L is a holomorphic line bundle. We will also drop the non-degeneracy assumption of the zeroes of s, but we treat only the case where s vanishes at isolated points {p}.

Suggested Citation

  • Paul F. Baum & Raoul Bott, 1970. "On the Zeroes of Meromorphic Vector-Fields," Springer Books, in: Essays on Topology and Related Topics, pages 29-47, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-49197-9_4
    DOI: 10.1007/978-3-642-49197-9_4
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