Celebratio Mathematica — Bott

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P. F. Baum and R. Bott: “On the zeroes of meromorphic vector-fields,” pp. 29–47 in Essays on topology and related topics: Mémoires dédiés à Georges de Rham [Essays on topology and related topics: Memoirs dedicated to Georges de Rham] (Geneva, 26–28 March 1969). Edited by A. Haefliger and R. Narasimhan. Springer (Berlin), 1970. MR 261635 Zbl 0193.52201 incollection

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 [Bott 1967]) 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 \( T\otimes L \) 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 \( \{p\} \).

Georges de Rham	Related
Paul Baum	Related	Volume
Raghavan Narasimhan	Related
André Haefliger	Related

P. Baum and R. Bott: “Singularities of holomorphic foliations,” J. Diff. Geom. 7 : 3–4 (1972), pp. 279–342. To S. S. Chern and D. C. Spencer on their 60th birthdays. MR 377923 Zbl 0268.57011 article

Donald Clayton Spencer	Related
S. S. Chern	Related	Volume
Paul Baum	Related	Volume

P. Baum: “Working with Bott (rocking and rolling with Raoul),” pp. xxii–xxiii in Raoul Bott: Collected papers, vol. 3: Foliations. Edited by R. MacPherson. Contemporary Mathematicians. Birkhäuser (Boston), 1995. MR 1321887 incollection

Paul Baum	Related	Volume
Robert Duncan MacPherson	Related