The tropical $j$-invariant TeX Export

@misc{citeulike:2617784, abstract = {If (Q,A) is a marked polygon with one interior point, then a general polynomial f in K[x,y] with support A defines an elliptic curve C on the toric surface X\_A. If K has a non-archimedean valuation into the real numbers we can tropicalize C to get a tropical curve Trop(C). If the Newton subdivision induced by f is a triangulation, then Trop(C) 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 C.}, archivePrefix = {arXiv}, author = {Katz, Eric and Markwig, Hannah and Markwig, Thomas}, citeulike-article-id = {2617784}, citeulike-linkout-0 = {http://arxiv.org/abs/0803.4021}, citeulike-linkout-1 = {http://arxiv.org/pdf/0803.4021}, day = {31}, eprint = {0803.4021}, keywords = {tropical}, month = {Mar}, posted-at = {2008-03-31 22:17:30}, priority = {2}, title = {The tropical \$j\$-invariant}, url = {http://arxiv.org/abs/0803.4021}, year = {2008} }

TY - ELEC ID - citeulike:2617784 L3 - citeulike-article-id:2617784 N2 - If (Q,A) is a marked polygon with one interior point, then a general polynomial f in K[x,y] with support A defines an elliptic curve C on the toric surface X_A. If K has a non-archimedean valuation into the real numbers we can tropicalize C to get a tropical curve Trop(C). If the Newton subdivision induced by f is a triangulation, then Trop(C) 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 C. TI - The tropical $j$-invariant KW - tropical AU - Katz, Eric AU - Markwig, Hannah AU - Markwig, Thomas PY - 2008/Mar/31/ UR - http://arxiv.org/abs/0803.4021 ER -