Tropical ideals of projective hypersurfaces

Abstract: A "tropical ideal", defined by Maclagan and Rincon, is an ideal in the tropical polynomial semiring that is also a tropical linear space (on each finite set of monomials). A tropical ideal cuts out a tropical variety. But already for projective tropical hypersurfaces there can be a large family of tropical ideal structures, much larger even than the set of tropicalisations of classical ideals. This talk will be centred on a collection of examples, including a non-realisable ideal structure on a large set of tropical hypersurfaces, and the classification of ideals of double points on the line.

This is based on joint work with Jeff and Noah Giansiracusa.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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