Minimal rational curves on complete toric manifolds

TL;DR

This paper demonstrates that the variety of minimal rational tangents on complete toric manifolds is linear and establishes a bijection between minimal components in the space of rational curves and primitive collections in the defining fan.

Contribution

It reveals a linear structure of minimal rational tangents and links minimal components to primitive collections in the fan, providing new geometric insights.

Findings

Variety of minimal rational tangents is linear on complete toric manifolds

Minimal components correspond bijectively to primitive collections

Establishes a geometric relationship between rational curves and fan combinatorics

Abstract

We shall show that the variety of minimal rational tangents on a complete toric manifold X is linear and minimal components in RatCurves^n(X) corresponds bijectively to some special primitive collections in the fan defining X.