THE TROPICAL j-INVARIANT
نویسندگان
چکیده
If (Q,A) is a marked polygon with one interior point, then a general polynomial f ∈ K[x, y] with support A defines an elliptic curve Cf on the toric surface XA. If K has a non-archimedean valuation into R we can tropicalize Cf to get a tropical curve Trop(Cf ). If the Newton subdivision induced by f is a triangulation, then Trop(Cf ) will be a graph of genus one and we show that the lattice length of the cycle of that graph is the negative of the valuation of the j-invariant of Cf .
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