GW Invariants Relative Normal Crossings Divisors

Abstract

In this paper we introduce a notion of symplectic normal crossings divisor V and define the GW invariant of a symplectic manifold X relative such a divisor. Our definition includes normal crossings divisors from algebraic geometry. The invariants we define in this paper are key ingredients in symplectic sum type formulas for GW invariants, and extend those defined in our previous joint work with T.H. Parker [IP1], which covered the case V was smooth. The main step is the construction of a compact moduli space of relatively stable maps into the pair (X, V) in the case V is a symplectic normal crossings divisor in X.

68 pages, 5 figures, revised version, many more details added based on referee reports

References in corpus (3)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Stable logarithmic maps to Deligne--Faltings pairs II
• Gromov Witten invariants of exploded manifolds

Cited by in corpus (7)

• A natural Gromov-Witten virtual fundamental class
• The Smoothability of Normal Crossings Symplectic Varieties
• Geometric transversality in higher genus Gromov-Witten theory
• Gluing formula for Gromov-Witten invariants in a triple product
• On the value of thinking tropically to understand Ionel's GW invariants relative normal crossing divisors
• Notes on exploded manifolds and a tropical gluing formula for Gromov-WItten invariants
• Log geometry and exploded manifolds