Enumeration of rational curves with cross-ratio constraints

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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–Siebert [14]. The proof is very short, involves only the standard theory of schemes, and works in arbitrary characteristic (including the mixed characteristic case).

Original languageEnglish
Pages (from-to)1356-1383
Number of pages28
JournalAdvances in Mathematics
Volume305
DOIs
StatePublished - 10 Jan 2017

Keywords

  • Algebraic and tropical geometry
  • Enumeration of rational curves

ASJC Scopus subject areas

  • Mathematics (all)

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