Rational curves on Fano threefolds with Gorenstein terminal singularities

Fumiya Okamura

Rational curves on Fano threefolds with Gorenstein terminal singularities

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arxiv 2401.15633 v3 pith:X7GGAU64 submitted 2024-01-28 math.AG

Fumiya Okamura This is my paper · ORCID

classification math.AG

keywords threefoldsfanoconjecturecurvesgeometricgorensteinmaninrational

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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.

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Moduli spaces of rational curves on Artin-Mumford double solids
math.AG 2025-01 conditional novelty 7.0 of 10

For each degree, the moduli space of rational curves on a general Artin-Mumford double solid has exactly two (for lines) or four (higher degrees) irreducible components, giving the first multiple-component verificatio...

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