Geometric Manin's conjecture and rational curves. (May 2019)

• Record Type: Journal Article
• Authors: Lehmann, Brian; Tanimoto, Sho
• Is Part Of: Compositio mathematica. Volume 155:Number 5(2019)
• Page Start: 833
• Page End: 862
• Publication Date: 2019-05
• Subjects: 14H10 (primary); rational curves, -- Manin's conjecture, -- Fujita invariant; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X19007103
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : Let $X$ be a smooth projective Fano variety over the complex numbers. We study the moduli space of rational curves on $X$ using the perspective of Manin's conjecture. In particular, we bound the dimension and number of components of spaces of rational curves on $X$ . We propose a geometric Manin's conjecture predicting the growth rate of a counting function associated to the irreducible components of these moduli spaces.