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GW Invariants Relative Normal Crossings Divisors

By Eleny-Nicoleta Ionel


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.Comment: 68 pages, 5 figures, revised version, many more details added based on referee report

Topics: Mathematics - Symplectic Geometry, Mathematics - Algebraic Geometry
Year: 2014
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