Timeline for How can complex abelian varieties degenerate to tropical abelian varieties
Current License: CC BY-SA 4.0
6 events
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Nov 27 at 13:09 | comment | added | divergent | @Nulhomologous : Thank you very much for your answer. Could you explain how we should interpret or change "to degenerate" here? I think somehow a half of the lattice should vanish and we consider the other half as a real lattice. Is this true? | |
Nov 26 at 13:10 | comment | added | Nulhomologous | About the case $g=1$, it is just to simplify. Any complex abelian variety can be express as $(\mathbb{C}^*)^g/\Lambda$ for some "lattice" $\Lambda$ (plus a polarization), by esentially taking $\exp(2\pi z)$ to the usual expression. | |
Nov 26 at 7:57 | comment | added | Nulhomologous | The problem here is that it is not true that a tropical abelian variety is a degeneration of a complex family: it is true in some sense over fields complete with respect to a non-archimedean valuation. Or if you change what it means "to degenerate". | |
Nov 23 at 13:00 | comment | added | divergent | @Nulhomologous Thank you very much. Could you more illustrate about this. In particular what is $q$ here? and why does this idea only works for elliptic curves i.e., $g=1$? | |
Nov 23 at 10:48 | comment | added | Nulhomologous | For $g=1$, the idea is to express your elliptic curve as $\mathbb{C}^*/q^{\mathbb{Z}}$. | |
Nov 23 at 8:54 | history | asked | divergent | CC BY-SA 4.0 |