Elliptic curves in honeycomb form
Abstract
A plane cubic curve, defined over a field with valuation, is in honeycomb form if its tropicalization exhibits the standard hexagonal cycle. We explicitly compute such representations from a given j-invariant with negative valuation, we give an analytic characterization of elliptic curves in honeycomb form, and we offer a detailed analysis of the tropical group law on such a curve.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.2356
- arXiv:
- arXiv:1203.2356
- Bibcode:
- 2012arXiv1203.2356C
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Combinatorics
- E-Print:
- 20 pages, 5 figures