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Results tagged with ag.algebraic-geometry
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user 158098
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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Bézout theorem for complex solutions of systems of homogeneous quaternionic polynomials
Suppose that I have a system of $n$ homogeneous polynomials in $n+1$ variables $p_{1},\dots,p_{n}\in\mathbb{H}[x_{0},\dots,x_{n}]$ with coefficients at both sides in $\mathbb{H}.$ I want to know if th …
- 573
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260
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Algebraic closure of field of fractions of multivariate polynomial ring over $\mathbb{R}$
I am searching for good references on the topic of the behaviour of the elements in the algebraic closed field $(\mathbb{R}[x_{1},\dots,x_{n}])^{\operatorname{alg}}.$ I imagine that, when we try to se …
- 573
2
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Topology of the set of polynomials with bounded real algebraic varieties (inside the v. s. o...
Set $x=(x_{1}, \dots, x_{n}).$ Consider the set $\mathbb{R}[x]_{d}$ of polynomials with coef. in $\mathbb{R}$ in $n$ variables up to degree $d.$ This set can be seen as a finite-dimensional vector spa …
- 573