Representants lagrangiens de l'homologie des surfaces projectives complexes

Details Representants lagrangiens de l'homologie des surfaces projectives complexes Representants lagrangiens de l'homologie des surfaces projectives complexes

2009-03-25

arxiv.org/abs/0903.4490v1

Mathematics

Differential Geometry

43 pages, 2 figures

Scientific paper

Using results by Donaldson and Auroux on pseudo-holomorphic curves as well as Duval's rational convexity construction, the paper investigates the existence of smooth Lagrangian surfaces representing 2-dimensional homology classes in complex projective surfaces. We prove that if the projective surface X is minimal, of general type, with uneven geometric genus, and has an effective, smooth and connected canonical divisor K, then there exists a non-empty convex open cone in the real 2-dimensional homology group H2(X) such that a multiple of every integral homology class in this cone can be represented by an embedded Lagrangian surface in X\K. A corollary asserts that such a surface X is of simple type in the sense of Kronheimer and Mrowka.

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