HIGHER JET EVALUATION TRANSVERSALITY OF J-HOLOMORPHIC CURVES
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In this paper, we establish general stratawise higher jet evalu-ation transversality of J-holomorphic curves for a generic choice of almost complex structures J (tame to a given symplectic manifold (M, ω)). Using this transversality result, we prove that there exists a subset <수식> of second category such that for every <수식>, the dimen-sion of the moduli space of (somewhere injective) J-holomorphic curves with a given ramification profile goes down by 2n or 2(n - 1) depending on whether the ramification degree goes up by one or a new ramification point is created. We also derive that for each <수식> there are only a finite number of ramification profiles of J-holomorphic curves in a given homology class β ∈ H_2(M ; Z) and provide an explicit upper bound on the number of ramification profiles in terms of c1(β) and the genus g of the domain surface.
Abstract
In this paper, we establish general stratawise higher jet evalu-ation transversality of J-holomorphic curves for a generic choice of almost complex structures J (tame to a given symplectic manifold (M, ω)). Using this transversality result, we prove that there exists a subset <수식> of second category such that for every <수식>, the dimen-sion of the moduli space of (somewhere injective) J-holomorphic curves with a given ramification profile goes down by 2n or 2(n - 1) depending on whether the ramification degree goes up by one or a new ramification point is created. We also derive that for each <수식> there are only a finite number of ramification profiles of J-holomorphic curves in a given homology class β ∈ H_2(M ; Z) and provide an explicit upper bound on the number of ramification profiles in terms of c1(β) and the genus g of the domain surface.
참고문헌 (10)
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