Reduced genus-two Gromov-Witten Invariants for complex manifolds

2008/12/13 by Wei Wang, Wang, Wei
Mathematics · #37K20 #53D30 #53D45 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.0812.2542

openalex publication_date 2008/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we construct the reduced genus-two Gromov-Witten invariants for certain almost Kähler manifold (X, ω, J) such that J is integrable and satisfies some regularity conditions. In particular, the standard projective space (¶ⁿ, ω₀, J₀) of dimension n ≤ 7 satisfies these conditions. This invariant counts the number of simple genus-two J-holomorphic curves that satisfy appropriate number of constraints.

Citations

• Symplectic manifolds with contact type boundaries
• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds

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