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<p>We study the spaces of rational curves on Fano threefolds with Gorenstein terminal singularities. We generalize the results regarding Geometric Manin’s Conjecture for smooth Fano threefolds, including the classification of subvarieties with higher <i>a</i>-invariants and Movable Bend-and-Break lemma. We also show Geometric Manin’s Conjecture for some singular del Pezzo threefolds.</p>

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Rational curves on Fano threefolds with Gorenstein terminal singularities

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • Fumiya Okamura

摘要

We study the spaces of rational curves on Fano threefolds with Gorenstein terminal singularities. We generalize the results regarding Geometric Manin’s Conjecture for smooth Fano threefolds, including the classification of subvarieties with higher a-invariants and Movable Bend-and-Break lemma. We also show Geometric Manin’s Conjecture for some singular del Pezzo threefolds.