English

Holomorphic curves in log-symplectic manifolds

Symplectic Geometry 2018-05-16 v2 Differential Geometry

Abstract

Log-symplectic structures are Poisson structures that are determined by a symplectic form with logarithmic singularities. We construct moduli spaces of curves with values in a log-symplectic manifold. Among the applications, we classify symplectically ruled log-symplectic 44 manifolds (both orientable and non-orientable), and obstruct the existence of contact boundary components, in analogy with well-known theorems by McDuff. Moreover, we study certain log-symplectically ruled surfaces, using tools from symplectic field theory.

Keywords

Cite

@article{arxiv.1711.10978,
  title  = {Holomorphic curves in log-symplectic manifolds},
  author = {Davide Alboresi},
  journal= {arXiv preprint arXiv:1711.10978},
  year   = {2018}
}

Comments

52 pages, major revision. one section totally rewritten and one theorem removed because of a mistake. one of the main results strengthened, one new theorem added