The number of ramified covering of the sphere by Riemann surface
نویسندگان
چکیده
Interpreting the number of ramified covering of the sphere by Riemann surface as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of the sphere by Riemann surface with any genus, with elementary branch points and prescribed ramification type over infinity.
منابع مشابه
The number of ramified covering of a Riemann surface by Riemann surface
Interpreting the number of ramified covering of a Riemann surface by Riemann surfaces as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of a Riemann surface by Riemann surface with elementary branch points and prescribed ramification type over a special point.
متن کاملSpatial statistics for lattice points on the sphere I: Individual results
We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares. We examine several statistics of these point sets, such as the electrostatic potential, Ripley's function, the variance of the number of points in random spherical caps, and the covering radius. Some of the results are conditional on t...
متن کاملCounting Meromorphic Functions with Critical Points of Large Multiplicities
We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is CP1 and the function is a polynomial, we give an elementary way of finding this number. In the general case, we show that, as the multiplicities of critical points tend to infinity, the asymptotic for the number of ...
متن کاملA Proof of a Conjecture for the Number of Ramified Coverings of the Sphere by the Torus
Let X be a compact connected Riemann surface of genus g"0. A ramified covering of S of degree n by X is a non-constant meromorphic function f : X!S such that | f (q)|=n for all but a finite number of points q # S, which are called branch points. Two ramified coverings f1 and f2 of S by X are said to be equivalent if there is a homeomorphism ? : X!X such that f1= f2 b?. A ramified covering f is ...
متن کاملRamified Coverings of the Riemann Sphere, Constellations, and Hypermaps on Surfaces
We review the theory of compact Riemann surfaces and connections between ramified coverings of the Riemann sphere, constellations, and hypermaps on surfaces. This note is based on the chapter 1 of [4].
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 1999