On Maximally Inflected Hyperbolic Curves
نویسندگان
چکیده
منابع مشابه
On Maximally Inflected Hyperbolic Curves
In this note we study the distribution of real inflection points among the ovals of a real non-singular hyperbolic curve of even degree. Using Hilbert’s method we show that for any integers d and r such that 4 ≤ r ≤ 2d − 2d, there is a non-singular hyperbolic curve of degree 2d in R with exactly r line segments in the boundary of its convex hull. We also give a complete classification of possib...
متن کاملMaximally Inflected Real Rational Curves
We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the real Schubert calculus, and their study has consequences for the important Shapiro and Shapiro conjecture in the real Schubert calculus. We establish restrictions on the number of real nodes of such curves and construc...
متن کاملCorrespondences on Hyperbolic Curves
We consider hyperbolic curves over an algebraically closed field k of characteristic zero. We call two such curves X, Y isogenous if there exists a nonempty scheme C , together with finite étale morphisms C → X, C → Y . (We refer to such a pair (C → X,C → Y ) as a correspondence from X to Y .) It is easy to see that the relation of isogeny is an equivalence relation on the set of isomorphism cl...
متن کاملSimple curves on hyperbolic tori
Let T be a once punctured torus, equipped with a complete hyperbolic metric. Herein, we describe a new approach to the study of the set S of all simple geodesics on T. We introduce a valuation on the homology H1(T,ZZ), which associates to each homology class h the length l(h) of the unique simple geodesic homologous to h, and show that l extends to a norm on H1(T,R). We analyze the boundary of ...
متن کاملOn the Combinatorial Cuspidalization of Hyperbolic Curves
In this paper, we continue our study of the pro-Σ fundamental groups of configuration spaces associated to a hyperbolic curve, where Σ is either the set of all prime numbers or a set consisting of a single prime number, begun in an earlier paper. Our main result may be regarded either as a combinatorial, partially bijective generalization of an injectivity theorem due to Matsumoto or as a gener...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2014
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-014-9603-8