A contraction theorem for divisors fibering over a curve

TL;DR

This paper establishes conditions under which a divisor fibering over a curve can be contracted in a bimeromorphic manner, with applications to contraction results in compact Kähler threefolds.

Contribution

It provides new sufficient conditions for contracting divisors fibering over a curve, extending contraction results to Kähler threefolds.

Findings

Sufficient conditions for divisor contraction over a curve

Application to contraction in compact Kähler threefolds

Extension of known contraction theorems

Abstract

Given a Q-Cartier divisor $S \subset X$ admitting a fibration $S \rightarrow B$ onto a curve we give sufficient conditions for the existence of a bimeromorphic contraction contracting S onto B. As a corollary we recover a contraction result for compact K\"ahler threefolds.