On negative spheres in elliptic surfaces

TL;DR

This paper explores the existence of spheres with highly negative self-intersections in elliptic surfaces, achieved through specific elliptic fibrations and their blow-ups, revealing new geometric configurations.

Contribution

It introduces a method to construct negative spheres in elliptic surfaces using particular singular fibers and blow-up techniques, advancing understanding of surface topology.

Findings

Existence of spheres with very negative self-intersections in elliptic surfaces

Construction method using specific singular fibers and blow-ups

New insights into the topology of elliptic surfaces

Abstract

Using elliptic fibrations with specific singular fibers, we find spheres with very negative self-intersections in elliptic surfaces and in their blow-ups.