A Note on the Effective Non-vanishing Conjecture

TL;DR

This paper uses Fourier-Mukai transform techniques to reduce the irregular case of the effective non-vanishing conjecture and confirms its validity on algebraic surfaces.

Contribution

It introduces a reduction method for the irregular case via Fourier-Mukai transform and reaffirms the conjecture on algebraic surfaces.

Findings

Effective non-vanishing conjecture holds on algebraic surfaces.

Reduction of irregular case achieved through Fourier-Mukai transform.

Reproves the conjecture using new approach.

Abstract

We give a reduction of the irregular case for the effective non-vanishing conjecture by virtue of the Fourier-Mukai transform. As a consequence, we reprove that the effective non-vanishing conjecture holds on algebraic surfaces.