Holomorphic Curves in Symplectic Geometry pp 191-215 | Cite as

# Singularities and positivity of intersections of *J*-holomorphic curves

Chapter

## Abstract

This chapter is devoted to proving some of the main technical results about *J*-holomorphic curves which make them such a powerful tool when studying the geometry of symplectic 4-manifolds. We begin by establishing some elementary local properties of these curves. Next, we develop enough of the theory of deformations of *J*-holomorphic curves to prove the following result in Gromov [2, 2.2.*C* _{2}] on the positivity of intersections of two curves in an almost complex 4-manifold.

## Keywords

Modulus Space Intersection Number Holomorphic Curve Holomorphic Curf Adjunction Formula
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