An introduction to Geometric Manin's conjecture

Abstract

This is a survey paper on Geometric Manin's conjecture which was proposed by Brian Lehmann and the author. We introduce Geometric Manin's conjecture (GMC) and review some recent progress on this conjecture.

The irreducibility of the spaces of rational curves on del Pezzo manifolds

“…In [24], the authors defined Manin components, which they propose should be counted in the conjectural asymptotic formula. For details about this conjecture, see [34] Definition 5.1 ([34] Definition 4.3). Let X be a weak Fano manifold.…”

“…A Manin component is a component which is not accumulating. Conjecture 5.2 (Geometric Manin's Conjecture ( [34])). Let X be a weak Fano manifold.…”