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Tropical refined curve counting from higher genera and lambda classes. (English) Zbl 07015696
Summary: Block and Göttsche have defined a \(q\)-number refinement of counts of tropical curves in \(\mathbb{R}^2\). Under the change of variables \(q=e^{iu}\), we show that the result is a generating series of higher genus log Gromov-Witten invariants with insertion of a lambda class. This gives a geometric interpretation of the Block-Göttsche invariants and makes their deformation invariance manifest.

MSC:
14T05 Tropical geometry (MSC2010)
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
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