All Questions
Tagged with graph-theory ag.algebraic-geometry
13 questions with no upvoted or accepted answers
15
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Grothendieck dessins d'enfants - current surveys or text you can recommend?
I was recommended this forum to be the leading site for algebraic geometry, so I would like to ask you a question about Grothendieck dessins d´enfants. My background is in maps on surfaces (graph ...
12
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325
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Is there an algorithm to compute a Belyi map for the Riemann surface?
Let $y^2=x^5-x-1$ be an affine model of a projective complex curve, is there an algorithm to compute the Belyi map (preferably of small degree), i.e., map to the projective line ramified only at $\{0,...
- 269
5
votes
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121
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The Smith decomposition of the graph Laplacian and Locality
Let $X$ be a graph. Let $V(X)$ and $E(X)$ be the sets of vertices and edges of the graph respectively. If $f:V(X) \rightarrow G$ where $G$ is an abelian group, then one can define a graph Laplacian as ...
- 51
5
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230
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Minimal algebraic degree of symmetric unit distance embedding of Heawood graph
I'm looking at embeddings of the Heawood graph in the plane as unit distance graph. Apparently the first such embedding was given by Gerbracht, 2009 and has algebraic (over the rationals) coordinates ...
- 10.7k
4
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127
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Measuring the failure of basepoint independence of the rotor-routing model for non-planar ribbon graphs
In this question from 2012, Jordan Ellenberg asks if the set of spanning trees of a graph $G$ is naturally a torsor for the critical group (also called the sandpile group or the picard group $Pic^0(G)$...
4
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972
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Questions about dessin d'enfants, trees and their Shabat polynomials
This will be a series of questions, a few of which have been troubling me for quite a while now. Before I jump right in, let me first introduce a few notions which I will assume.
(Note: All of these ...
- 829
3
votes
0
answers
157
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F-vectors of simplicial complex and f-vectors of non-faces of simplicial complex
Is there any result which gives us a relation between f-vector of simplicial complex and f-vector of nonfaces of a simplicial complex?
Thank you
- 51
3
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0
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190
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Construction of algebraic curves using line bundles on graphs
In this paper http://arxiv.org/abs/0707.1309 Matthew Baker and Serguei Norine, construct a analogue of the Riemman Roch formula for Lineal Systems defined on graphs. In the paper http://arxiv.org/abs/...
- 527
3
votes
0
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98
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Reconstructing a function from its variants that negate one argument
Call two functions $g(x_1,\ldots,x_n)$ and $h(x_1,\ldots,x_n)$ from complex numbers to complex numbers equivalent if they are the same up to the order of their arguments. Formally: there is a ...
- 37.7k
2
votes
0
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143
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Optimization over Spectral Laplacian in cycles and trees
Is there any idea on how one can deal with an optimization problem of sum of k largest eigenvalues(min) of Laplacian matrix of a simple cycle or tree?
I would like to use semidefinite programming for ...
- 161
1
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100
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Varieties determined by a characteristic-type of polynomial with the structure of an underlying graph
While writing my master thesis, following problem came up:
Given a digraph $G$ with edges $e_1,..,e_n$ and a
given a $n\times n$- matrix $A\in\mathbb{C}^{n\times n}$ such that $A_{ij}=0$ if the ending ...
- 33
0
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0
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64
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Relation between a cycle on a toroidal graph and divisors of elliptic curve over complex plane
I am very new to algebraic geometry. I was reading about divisors on a scheme. I am wondering does there is some connection between the followings.
An elliptic curve over the complex plane we can ...
- 613
0
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0
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57
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Reference for packing property and König property
Can someone please suggest reference material to study about the packing property and König property of ideals and some examples?
- 21