Enumeration of rational curves with cross-ratio constraints

Abstract

In this paper we prove the algebraic-tropical correspondence for stable maps of rational curves with marked points to toric varieties such that the marked points are mapped to given orbits in the big torus and in the boundary divisor, the map has prescribed tangency to the boundary divisor, and certain quadruples of marked points have prescribed cross-ratios. In particular, our results generalize the results of Nishinou and Siebert. The proof is very short, involves only the standard theory of schemes, and works in arbitrary characteristic (including the mixed characteristic case).

23 pages, 5 figures. To appear in Adv.Math

References in corpus (2)

• Enumerative tropical algebraic geometry in R2
• Moduli spaces of rational tropical curves

Cited by in corpus (6)

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• Tropical $\psi$ classes
• Computation of refined toric invariants II