I wanted read about Dessign d' enfants most of the reference define it as (X,D) where X is compact orientable surface and D is the bipartite graph with some properties that is there is a bijection with covering map over $\mathbb{P}^1$ having $0,1,\infty$ as branch point. I want to know if there is an immediate generalisation with $\mathbb{P}^1$ having any finite number of branch point. Please give a reference. The result I am chasing is some this like this if for the three point case let $\sigma_0$ , $\sigma_1$ and $\sigma_{\infty}$ are the ramification profile for the over $0,1,\infty$ and $\sigma_0\sigma_1\sigma_{\infty}=id$ then there is a dessign corresponding to this data and its a bipartite graph, so is it true that if we increase the branch point say 4 branch point the dessign will look like tripartite graph ?
2026-03-27 10:15:42.1774606542
More than 3 branch point Dessign d' enfant
84 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in RIEMANN-SURFACES
- Composing with a biholomorphic function does not affect the order of pole
- open-source illustrations of Riemann surfaces
- I want the pullback of a non-closed 1-form to be closed. Is that possible?
- Reference request for Riemann Roch Theorem
- Biholomorphic Riemann Surfaces can have different differential structure?
- Monodromy representations and geodesics of singular flat metrics on $\mathbb{H}$
- How to choose a branch when there are multiple branch points?
- Questions from Forster's proof regarding unbranched holomorphic proper covering map
- Is the monodromy action of the universal covering of a Riemann surface faithful?
- Riemann sheets for combined roots
Related Questions in COMBINATORIAL-GEOMETRY
- Properties of triangles with integer sides and area
- Selecting balls from infinite sample with certain conditions
- Number of ways to go from A to I
- A Combinatorial Geometry Problem With A Solution Using Extremal Principle
- Find the maximum possible number of points of intersection of perpendicular lines
- The generous lazy caterer
- Number of paths in a grid below a diagonal
- How many right triangles can be constructed?
- What is the exact value of the radius in the Six Disks Problem?
- Why are there topological no results on halfspace arrangements?
Related Questions in SEVERAL-COMPLEX-VARIABLES
- Let $h(z) = g(f(z))$. If $f$ and $h$ are non-constant holomorphic function on domains in $\mathbb C^n$, then is $g$ holomorphic?
- If power series in two variables and logarithmically convex Reinhardt domains
- Product of holomorphically convex spaces is again holomorphically convex
- Differential Geometry tools in Several Complex Variables
- Is the complement of a complex affine algebraic set in an irreducible complex affine algebraic set (path) connected in the euclidean topology?
- Any entire holomorphic function that is bounded on countably infinite number of complex-lines must be constant.
- Do there exist infinitely many complex lines through the origin?
- Can a pure codimension d analytic subset be defined by a d-tuple of holomorphic functions?
- How to show $\int_{0}^{\infty} \frac{dx}{x^3+1} = \frac{2\pi}{3\sqrt{3}}$
- Build a Blaschke product such as $B^*(1)=\lim_{r\to 1}B(r)=0$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Grothendieck has defined Dessins d'enfants to study non singular curves defined over $\bar Q$ the algebraic closure of $Q$, it turns out that Belyi has shown that for such a curve $C$, there is always a map $f:C\rightarrow P^1C$ ramified at at most 3 points, so there is no need to study the situation where the number of branch points is stricly superior to 3.
https://en.wikipedia.org/wiki/Belyi%27s_theorem