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Toward Gromov-Witten Invariants for Relatively Coherent Logarithmic Schemes

  • Author(s): Kasa, Michael Paul
  • et al.
Abstract

A theory of logarithmic Gromov-Witten invariants has been developed by Gross- Siebert for logarithmically smooth targets [GS13] and by Abramovich-Chen for Deligne-Faltings pairs [AC14]. We begin to extend these theories to the setting of relatively coherent targets; such a theory is needed for application to the Gross-Siebert program [Gro10]. We describe the conjecturally-algebraic stack of stable log maps to relatively coherent targets, and we give an analogue of basicness which selects a substack of stable maps with minimal log structures. We present two example calculations which apply our theory to classical curve counting problems. Finally, we give an algorithm for resolving a relatively coherent log scheme of the type appearing in the Gross-Siebert program [GS10] to a fine log scheme via toric blowups

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