Symplectic Classes on Elliptic Surfaces with positive Euler Number

Josef G. Dorfmeister; Tian-Jun Li

Symplectic Classes on Elliptic Surfaces with positive Euler Number

Symplectic Geometry 2026-04-30 v2 Algebraic Geometry Geometric Topology

Authors: Josef G. Dorfmeister , Tian-Jun Li

Abstract

A key question for $4$ -manifolds $M$ admitting symplectic structures is to determine which cohomology classes $\alpha\in H^2(M,\mathbb R)$ admit a symplectic representative. The collection of all such classes, the symplectic cone $\mathcal C_M$ , is a basic smooth invariant of $M$ . This paper describes the symplectic cone for elliptic surfaces with positive Euler number.

Keywords

symplectic geometry smooth 4-manifolds elliptic curves

Cite

@article{arxiv.2507.20940,
  title  = {Symplectic Classes on Elliptic Surfaces with positive Euler Number},
  author = {Josef G. Dorfmeister and Tian-Jun Li},
  journal= {arXiv preprint arXiv:2507.20940},
  year   = {2026}
}

Comments

54 pages. Comments welcome! (This version differs from an earlier version by changing the focus from elliptic surfaces without multiple fibers to elliptic surfaces with positive Euler number.)

Symplectic Classes on Elliptic Surfaces with positive Euler Number

Abstract

Keywords

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