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Paper IPM / M / 16147  


Abstract:  
Given a symplectic threefold (M,ω) we
show that for a generic almost complex structure J
which is compatible with ω,
there are finitely many Jholomorphic curves in M of any genus g ≥ 0
representing a homology class β in \Ht_{2}(M,\Z)
with c_{1}(M).β = 0, provided that the divisibility of β is at most 4 (i.e.
if β = nα with α ∈ \Ht_{2}(M,\Z) and n ∈ \Z then n ≤ 4).
Moreover, each such curve is embedded and 4rigid.
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