Effective bounds for the number of MMP-series of a smooth threefold

TL;DR

This paper establishes an upper bound of two on the number of MMP-series for certain smooth projective threefolds with positive Kodaira dimension and Picard number three, advancing understanding of their birational geometry.

Contribution

It provides a new bound on the number of MMP-series for a specific class of threefolds, which was previously unknown.

Findings

Number of MMP-series is at most two for the specified threefolds.

The result applies to threefolds with positive Kodaira dimension and Picard number three.

Abstract

We prove that the number of MMP-series of a smooth projective threefold of positive Kodaira dimension and of Picard number equal to three is at most two.