# Duality Spectral Sequences for Weierstrass Fibrations and Applications

## TL;DR

This paper explores duality spectral sequences in Weierstrass fibrations, demonstrating that certain line bundles are transformed into slope stable sheaves via Fourier-Mukai transforms on specific threefolds.

## Contribution

It introduces the use of duality spectral sequences in the context of Weierstrass fibrations and characterizes the Fourier-Mukai transform behavior on K-trivial threefolds.

## Key findings

- Line bundles of nonzero fiber degree are transformed into slope stable sheaves.
- Spectral sequences provide new insights into the structure of sheaves on Weierstrass fibrations.
- The results apply to K-trivial Weierstrass threefolds over K-numerically trivial surfaces.

## Abstract

We study duality spectral sequences for Weierstrass fibrations. Using these spectral sequences, we show that on a K-trivial Weierstrass threefold over a K-numerically trivial surface, any line bundle of nonzero fiber degree is taken by a Fourier-Mukai transform to a slope stable locally free sheaf.