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Orientations and Geometrisations of Compact Complex Surfaces
Author(s) -
Kotschick D.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002287
Subject(s) - mathematics , manifold (fluid mechanics) , signature (topology) , orientation (vector space) , zero (linguistics) , pure mathematics , reversing , wonder , topology (electrical circuits) , geometry , combinatorics , mechanical engineering , psychology , social psychology , linguistics , philosophy , materials science , engineering , composite material
Every complex manifold carries a canonical orientation, and it is natural to wonder when the underlying topological or smooth manifold carries a complex structure compatible with the other orientation. In [ 2 ], Beauville raised this question for compact complex surfaces. He noted that there are a lot of examples, like products of curves, or Hopf surfaces, where the underlying manifold admits an orientation‐reversing selfdiffeomorphism. This implies that the signature is zero. Beauville asked if there are any examples of non‐zero signature. 1991 Mathematics Subject Classification 14J99, 53C55, 53C15.