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Tropical refined curve counting from higher genera and lambda classes
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abstract
Block and G\"ottsche 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-G\"ottsche invariants and makes their deformation invariance manifest.
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BPS polynomials and Welschinger invariants
The new BPS polynomials of surfaces specialize at q=-1 to Welschinger invariants for blowups of the projective plane at up to six points.
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