The number of smooth varieties in an MMP on a 3-fold of Fano type

2025/02/03 by Kim, Donghyeon · 2 citations
#14E30 #14F17 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.01370

Abstract

In this paper, we prove that for a threefold of Fano type X and a movable ℚ-Cartier Weil divisor D on X, the number of smooth varieties that arise during the running of a D-MMP is bounded by 1 + h¹(X, 2D). Additionally, we prove a partial converse to the Kodaira vanishing theorem for a movable divisor on a threefold of Fano type.

Cited by

• Forms and Complex Manifolds
• Effective termination of general type MMPs in dimension at most five

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