Rational curves in Fano hypersurfaces and tropical curves

2011/08/14 by Takeo Nishinou, Nishinou, Takeo
Computer Science · Mathematics · #Polynomial and algebraic computation #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.1108.2860

Abstract

Using ideas from the theory of tropical curves and degeneration, we prove that any Fano hypersurface (and more generally Fano complete intersections) is swept by at most quadratic rational curves.

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• Balanced rational curves and minimal rational connectedness of Fano hypersurfaces
• Lines, conics, and all that
• Rational surfaces in index-one Fano hypersurfaces
• Very free rational curves in Fano varieties
• Low-degree Rational curves on hypersurfaces in projective spaces and their degenerations