Combinatorics of tropical Hurwitz cycles
نویسندگان
چکیده
منابع مشابه
Combinatorics of Tropical Hurwitz Cycles
We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points the resulting cycles are weakly irreducible, i.e. an integer multiple of an irreducible cycle. We study how Hurwitz cycles can be written as div...
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Hurwitz numbers count genus g, degree d covers of P1 with fixed branch locus. This equals the degree of a natural branch map defined on the Hurwitz space. In tropical geometry, algebraic curves are replaced by certain piece-wise linear objects called tropical curves. This paper develops a tropical counterpart of the branch map and shows that its degree recovers classical Hurwitz numbers. Furthe...
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The tropical semi-ring is the triplet (R,⊕, ) with x⊕ y := min(x,y) and x y := x+ y . Its algebraic properties are somewhat modest, if one compares it with rings and fields, which are more common in most areas of mathematics. Still the distributive laws hold, and as an additional catch the addition is idempotent, that is, x⊕ x = x holds for all x ∈ R. As defined our tropical semi-ring is lackin...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2015
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-015-0615-0