English

Log geometry and exploded manifolds

Symplectic Geometry 2012-06-08 v4 Algebraic Geometry

Abstract

Log Gromov-Witten invariants have recently been defined separately by Gross and Siebert and Abramovich and Chen. This paper provides a dictionary between log geometry and holomorphic exploded manifolds in order to compare Gromov-Witten invariants defined using exploded manifolds or log schemes. The gluing formula for Gromov-Witten invariants of exploded manifolds suggests an approach to proving analogous gluing formulas for log Gromov-Witten invariants.

Keywords

Cite

@article{arxiv.1108.3713,
  title  = {Log geometry and exploded manifolds},
  author = {Brett Parker},
  journal= {arXiv preprint arXiv:1108.3713},
  year   = {2012}
}

Comments

v4: In previous versions, I used C[Q/Q'] to mean the quotient of C[Q] by the ideal generated by Q' in the mistaken belief that this was equal to the monoid ring over Q/Q'. The offending notation is now fixed

R2 v1 2026-06-21T18:52:21.190Z