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arXiv · 2609.18936

Relative cone of curves and extremal contractions of a successive blowup

Yuto Masamura
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Abstract

Let $X$ be a normal variety, and let $π\colon\tilde X\to X$ be the successive blowup along subvarieties $Z_1,\dotsc,Z_n\subseteq X$ of codimension at least two that have simple normal crossings and satisfy $Z_h\not\supseteq Z_i$ whenever $h<I$. We prove that the relative cone of curves $\overline{\operatorname{NE}}(\tilde X/X)$ is generated by the classes of finitely many elementary curves, and that every face admits a contraction over $X$. We describe the exceptional loci of extremal ray contractions, and prove that every small extremal ray contraction admits a $D$-flip for every $\mathbb R$-Cartier divisor $D$ negative on the corresponding ray.

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Yuto Masamura. 2026-09-16. Relative cone of curves and extremal contractions of a successive blowup. https://arxiv.org/abs/2609.18936

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