Rational curves on hypersurfaces of low degree

DOI10.1515/crll.2004.045zbMath1052.14027arXivmath/0203088OpenAlexW2023076883MaRDI QIDQ4810850

Mike Roth, Joe Harris, Jason Michael Starr

Publication date: 17 August 2004

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0203088

zbMATH Keywords

stacksHilbert schemesdual graphsKontsevich moduli spaces of stable maps

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Parametrization (Chow and Hilbert schemes) (14C05) Algebraic moduli problems, moduli of vector bundles (14D20) Hypersurfaces and algebraic geometry (14J70)

Related Items (31)

Linear subspaces of hypersurfaces ⋮ Higher Fano manifolds and rational surfaces ⋮ Rational curves on smooth hypersurfaces of low degree ⋮ Moduli spaces of rational curves on Fano threefolds ⋮ Geometric consistency of Manin's conjecture ⋮ RATIONAL CURVES ON CUBIC HYPERSURFACES OVER FINITE FIELDS ⋮ Positivity results for spaces of rational curves ⋮ Low-degree rational curves on hypersurfaces in projective spaces and their fan degenerations ⋮ An introduction to rationally connected fibrations over curves and surfaces ⋮ Fields of definition of rational curves of a given degree ⋮ Classifying sections of del Pezzo fibrations. I ⋮ Free rational curves on low degree hypersurfaces and the circle method ⋮ Rational curves on general type hypersurfaces ⋮ Geometric Manin’s conjecture and rational curves ⋮ Hypersurfaces with too many rational curves ⋮ The irreducibility of the spaces of rational curves on del Pezzo surfaces ⋮ Kontsevich spaces of rational curves on Fano hypersurfaces ⋮ Rational curves on blowing-ups of projective spaces ⋮ A note on gonality of curves on general hypersurfaces ⋮ 2-cycles on higher Fano hypersurfaces ⋮ Moduli spaces of curves and Cox rings ⋮ Incident rational curves ⋮ Quadratic solutions of quadratic forms ⋮ A note on rational curves on general Fano hypersurfaces ⋮ On Fano Schemes of Complete Intersections ⋮ Dimension of the space of conics on a Fano hypersurface ⋮ On exceptional sets in Manin's conjecture ⋮ A remark on the intersection of plane curves ⋮ Rational curves on prime Fano threefolds of index 1 ⋮ Classifying sections of del Pezzo fibrations. II ⋮ The spaces of rational curves on del Pezzo threefolds of degree one

Cites Work

• Notes on stable maps and quantum cohomology
• Unnamed Item

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