Tropical compactification and the Gromov–Witten theory of P1

• Renzo Cavalieri ^[1] ; Hannah Markwig ^[2] ; Dhruv Ranganathan ^[3]
  1. [1] Colorado State University

     Colorado State University

     Estados Unidos

     
  2. [2] University of Tübingen

     University of Tübingen

     Landkreis Tübingen, Alemania

     
  3. [3] Yale University

     Yale University

     Town of New Haven, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1027-1060
• Idioma: inglés
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• Resumen

  • We use tropical and non-archimedean geometry to study the moduli space of genus 0, stable maps to P1 relative to two points. This space is exhibited as a tropical compactification in a toric variety. Moreover, the fan of this toric variety may be interpreted as a moduli space for tropical relative stable maps with the same discrete data. As a consequence, we confirm an expectation of Bertram and the first two authors, that the tropical Hurwitz cycles are tropicalizations of classical Hurwitz cycles. As a second application, we obtain a full descendant correspondence for genus 0 relative invariants of P1.