The Relative Symplectic Cone and T^2-Fibrations

TL;DR

This paper introduces the concept of the relative symplectic cone and applies it to determine the symplectic cone of specific T^2-fibrations, confirming a conjecture for certain elliptic surfaces.

Contribution

It defines the relative symplectic cone and uses it to compute the symplectic cone of T^2-fibrations, verifying a conjecture for some elliptic surfaces.

Findings

Determined the symplectic cone for certain T^2-fibrations.

Verified a conjecture on the symplectic cone of minimal Kähler surfaces.

Introduced the notion of the relative symplectic cone.

Abstract

In this note we introduce the notion of the relative symplectic cone. As an application, we determine the symplectic cone of certain T^2-fibrations. In particular, for some elliptic surfaces we verify a conjecture on the symplectic cone of minimal Kaehler surfaces raised by the second author.