On the log–local principle for the toric boundary

Abstract

Let be a smooth projective complex variety and let = 1 + + be a reduced normal crossing divisor on with each component smooth, irreducible and numerically effective. The log-local principle put forward in van Garrel et al. (Adv. Math. 350 (2019) 860-876) conjectures that the genus 0 log Gromov-Witten theory of maximal tangency of (, ) is equivalent to the genus 0 local Gromov-Witten theory of twisted by =1 (- ). We prove that an extension of the loglocal principle holds for a (not necessarily smooth) -factorial projective toric variety, the toric boundary, and descendant point insertions. M S C ( 2 0 2 0 ) 14N35 (primary), 14M25, 14J33, 14T90 (secondary) 1

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