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Results tagged with ag.algebraic-geometry
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user 23827
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
6
votes
Are there any known criteria for quadratic mapping from R^n to R^n being surjective?
If $n=2$ the quadratic map $\mathbb{R}^2\to\mathbb{R}^2$ with $(x_1,x_2)\mapsto (x_1^2-x_2^2,2x_1x_2)$ is surjective. This follows because the map $\mathbb{C}\to\mathbb{C}$ with $z\mapsto z^2$ is surj …
- 1,991
3
votes
1
answer
288
views
Number of solutions of a degree 4 polynomial equation over a finite field
Suppose that $q$ is a prime power and $\xi, \eta\in \mathbb{F}_q$ are nonzero. A computer calculation for $q<70$ suggests that the number $N$ of $4$-tuples
$(a,b,c,d)\in\mathbb{F}_q^{4}$ satisfying $( …
- 1,991