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Paper   IPM / M / 16147
School of Mathematics
  Title:   On finiteness and rigidity of J-holomorphic curves in symplectic three-folds
  Author(s):  Eaman Eftekhary
  Status:   Published
  Journal: Adv. Math.
  Vol.:  289
  Year:  2016
  Pages:   1082-1105
  Supported by:  IPM
Given a symplectic three-fold (M,ω) we show that for a generic almost complex structure J which is compatible with ω, there are finitely many J-holomorphic curves in M of any genus g ≥ 0 representing a homology class β in \Ht2(M,\Z) with c1(M).β = 0, provided that the divisibility of β is at most 4 (i.e. if β = nα with α ∈ \Ht2(M,\Z) and n ∈ \Z then n ≤ 4). Moreover, each such curve is embedded and 4-rigid.

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