-holomorphic curves in almost complex surfaces do not always minimize the genus

Author:
G. Mikhalkin

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1831-1833

MSC (1991):
Primary 57R95, 53C15

MathSciNet review:
1363430

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Abstract: The adjunction formula computes the genus of an almost complex curve embedded in an almost complex surface in terms of the homology class of . If is Kähler (or at least symplectic) and the self-intersection of is non-negative then the genus of any other surface embedded in and homologous to is not less then the genus of (the proof of this statement (which is a generalization of the Thom conjecture for ) was recently given by the Seiberg-Witten theory). This paper shows that the extra assumptions on are essential for the genus-minimizing properties of embedded almost complex curves.

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Additional Information

**G. Mikhalkin**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 1A1

Email:
mihalkin@math.toronto.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-97-03710-6

Received by editor(s):
September 22, 1995

Communicated by:
Ronald Stern

Article copyright:
© Copyright 1997
American Mathematical Society