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Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves
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abstract
We introduce algebraic structures on the polyvector fields of an algebraic torus that serve to compute multiplicities in tropical and log Gromov-Witten theory while also connecting to the mirror symmetry dual deformation theory of complex structures. Most notably these structures include a tropical quantum field theory and an $L_{\infty}$-structure. The latter is an instance of Getzler's gravity algebra, and the $l_2$-bracket is a restriction of the Schouten-Nijenhuis bracket. We explain the relationship to string topology in the appendix (thanks to Janko Latschev).
Forward citations
Cited by 2 Pith papers
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Sheaves of maximal intersection and multiplicities of stable log maps
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On the log-local principle for the toric boundary
For Q-factorial projective toric varieties whose toric boundary divisors are nef, the genus-zero log and local Gromov-Witten invariants with point and descendant insertions agree after the log-local normalization, and...
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