# Questions tagged [genus]

The tag has no usage guidance.

24 questions
Filter by
Sorted by
Tagged with
106 views

### Integral solutions to f(x, y, z) = n where f is a cubic form

I'm looking to see if there is an integral solution to $f(x,y,z)=n$ where f is a cubic form. Especially interesting is the diagonal case: $$ax^3+by^3+cz^3=n$$ for fixed integers $a,b,c,n$. If there ...
97 views

### Where can I find a picture of the complete 9-map on a triple torus that corresponds to Heffter’s table?

What I’m looking for is the analogue of Figure 5 in the paper by Saul Stahl, The Othe Map Coloring Theorem, Mathematics Magazine 1985, which is a complete 8-map $M_8$ on the double torus $S_2$ that ...
1 vote
42 views

### Is there an effective genus theory for indefinite quadratic forms?

For positive definite quadratic forms, there is a way to check if two forms are isomorphic by arithmetic equivalence over $GL_n(Z)$ by computing configurations of vector up to some norm and then ...
1 vote
111 views

554 views

### Hyperelliptic Curve [closed]

Consider the curve given by $z^{2g-2}y^2=\displaystyle\prod_{i=1}^{2g}(x-a_iz)$. This is a hyperelliptic curve and has genus $g-1$. At the same time it is a curve defined by an equation of $d=2g$ and ...
498 views

262 views

### smooth curves of genus 3 over an algebraic closed field

Is there a way to "easily" compute and describe the Moduli space of smooth curves of genus 3 without stacks and stable curves? In Hartshorne's Algebraic Geometry there is a nice excercise (Chapter ...
1k views

### Genus and Spinor genus of a lattice

Hi, I'm looking for a motivation for the names genus and spinor genus of a lattice (and spinor norm of an isometry). Is there any relation between the genus of a lattice and the genus of an algebraic ...