{"ID":23003496,"CreatedAt":"2026-09-17T04:20:54.235930923Z","UpdatedAt":"2026-09-17T04:20:54.235930923Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18936","arxiv_id":"2609.18936","title":"Relative cone of curves and extremal contractions of a successive blowup","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 $h\u003cI$. 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.","short_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 $h\u003cI$. We prove that the relative cone of curves $\\overline{\\operatorname{NE}}(\\ti...","url_abs":"https://arxiv.org/abs/2609.18936","url_pdf":"https://arxiv.org/pdf/2609.18936v1","authors":"[\"Yuto Masamura\"]","published":"2026-09-16T17:09:15Z","proceeding":"math.AG","tasks":"[\"math.AG\"]","methods":"[]","has_code":false}