Some examples on moduli spaces of low degree rational curves on low degree complete intersections

2011/10/27 by Pan, Xuanyu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1110.5965

Abstract

This paper is to give some concrete examples of the general fibers of the evaluation map of some Kontsevich mapping spaces parametrize low degree rational curves on low degree complete intersection varieties. We prove these examples are Fano or Calabi-Yau vareities of low dimension, e.g, surface and threefold. In usual, the "moduli" fibers are constructed in an abstract way, but here we give a down-to-earth interpretation to some of these fibers from the perspective of projective geometry.

Related

• Geometry of Rational Curves on Low degree Complete Intersections
• Rational curves on hypersurfaces of low degree
• Rational curves on complete intersections and the circle method
• Low-degree Rational curves on hypersurfaces in projective spaces and their degenerations
• The Kodaira dimension of spaces of rational curves on low degree hypersurfaces