2019/12/13 by Thomas Blomme, Blomme, Thomas · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1912.06453
openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
G. Mikhalkin introduced a refined count for real rational curves in a toric surface which pass through some points on the toric boundary of the surface. The refinement is provided by the value of a so-called quantum index. Moreover, he proved that the result of this refined count does not depend on the choice of the points. The correspondence theorem allows one to compute these invariants using the tropical geometry approach and the refined Block-Göttsche multiplicities. In this paper we give a recursive formula for these invariants, that leads to an algorithm to compute them.