Geometry of Rational Curves on Low degree Complete Intersections

2013/10/13 by Xuanyu Pan, Pan, Xuanyu
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1310.3506

openalex publication_date 2013/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a smooth complete intersection X, we consider a general fiber \mathbbF of the evaluation map ev of Kontsevich moduli space M_0,m(X,m)→ X^m and the forgetful functor F : \mathbbF → M_0,m. We prove that a general fiber of the map F is a smooth complete intersection if X is of low degree. The result sheds some light on the arithmetic and geometry of Fano complete intersections.

Related

• Some examples on moduli spaces of low degree rational curves on low degree complete intersections
• Rational curves on hypersurfaces of low degree
• Rational curves on complete intersections and the circle method
• Kontsevich spaces of rational curves on Fano hypersurfaces
• On the arithmetic of weighted complete intersections of low degree