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Summary: Estimated transversality in
symplectic geometry and
projective maps
Denis AUROUX
Ample bundles over almost-complex
manifolds
GW invariants: holomorphic maps from complex man-
ifolds to a symplectic manifold
Dual point of view: (approx.) holomorphic maps from a
symplectic manifold to complex manifolds (Donaldson)
Tool: estimated transversality for approx. holomorphic
sections of very ample bundles
( good linear systems, maps to CPm
)
(X2n
, J) almost-complex, compact
(Lk, k) line bundles are asympt. very ample if
curvature
iFk(v, Jv) > ck|v|2
, ck +
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