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arXiv · 2502.01370

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

Donghyeon Kim
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Abstract

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

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Donghyeon Kim. 2025-02-03. The number of smooth varieties in an MMP on a 3-fold of Fano type. https://doi.org/10.11650/tjm%2F251101

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