On the value of thinking tropically to understand Ionel's GW invariants relative normal crossing divisors
arXiv:1407.3020
Abstract
Ionel's GW invariants relative normal-crossing divisors appear different from Gromov-Witten invariants defined using log schemes or exploded manifolds. Appearances are, in this case, deceiving. I sketch the relationship between Ionel's invariants and their exploded cousins using the example of the moduli space of lines in the complex projective plane relative two coordinate lines. Even in this simplest of examples, 13 different types of curves appear in Ionel's compactified moduli space, but these different types of curves can be understood in a unified and intuitive fashion using tropical curves.
16 pages, mostly pictures
References in corpus (8)
- Gromov Witten invariants of exploded manifolds
- The Evaluation Space of Logarithmic Stable Maps
- Holomorphic curves in exploded manifolds: Kuranishi structure
- Gluing formula for Gromov-Witten invariants in a triple product
- Comparison theorems for Gromov-Witten invariants of smooth pairs and of degenerations
- The degeneration formula for logarithmic expanded degenerations
- Universal tropical structures for curves in exploded manifolds
- Tropical enumeration of curves in blowups of the projective plane