Duality of Tropical Curves
نویسنده
چکیده
Duality of curves is an important aspect of the “classical” algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using the development of an algebraic “mechanism”, based on “distortion” values, geometric and convexity properties are analyzed. Specifically, we discuss some significant aspects referring to quadrics with respect to their dual objects. This topic also includes the induced dual subdivision of the corresponding Newton Polytope and its compatible properties. Finally, a regularity of tropical curves in the duality sense is generally defined and studied for families of tropical quadrics.
منابع مشابه
Polynomiality, wall crossings and tropical geometry of rational double Hurwitz cycles
We study rational double Hurwitz cycles, i.e. loci of marked rational stable curves admitting a map to the projective line with assigned ramification profiles over two fixed branch points. Generalizing the phenomenon observed for double Hurwitz numbers, such cycles are piecewise polynomial in the entries of the special ramification; the chambers of polynomiality and wall crossings have an expli...
متن کاملString networks as tropical curves
A prescription for obtaining supergravity solutions for planar (p, q)-string networks is presented, based on earlier results. It shows that networks may be looked upon as tropical curves emerging as the spine of the amoeba of a holomorphic curve in M-theory. The Kähler potential of supergravity is identified with the corresponding Ronkin function. Implications of this identification in counting...
متن کاملTropical Curves
A tropical curve is a graph with specified edge lengths, some of which may be infinite. Various facts and attributes about algebraic curves have analogs for tropical curves. In this article, we focus on divisors and linear series, and prove the Riemann-Roch formula for divisors on tropical curves. We describe two ways in which algebraic curves may be transformed into tropical curves: by aboemas...
متن کاملDiagonal walks on plane graphs and local duality
We introduce the notion of local duality for planarmaps, i.e., for graphs embedded in the plane. Local duality is the transitive closure of the relation that transforms a graph that is the union of two connected subgraphs sharing a vertex by dualizing one of the two subgraphs. We prove that two planar maps have the same diagonal walks iff one of them can be transformed into the other by applyin...
متن کاملThe Chern Classes of the Verlinde Bundles
A formula for the first Chern class of the Verlinde bundle over the moduli space of smooth genus g curves is given. A finite-dimensional argument is presented in rank 2 using geometric symmetries obtained from strange duality, relative Serre duality, and Wirtinger duality together with the projective flatness of the Hitchin connection. A derivation using conformal-block methods is presented in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005