The geometry of points on quantum projectivizations

Details The geometry of points on quantum projectivizations The geometry of points on quantum projectivizations

2009-03-02

arxiv.org/abs/0903.0352v1

J. Algebra 246 (2001), 761-792

Mathematics

Algebraic Geometry

25 pages

Scientific paper

Suppose $S$ is an affine, noetherian scheme, $X$ is a separated, noetherian $S$-scheme, $\mathcal{E}$ is a coherent ${\mathcal{O}}_{X}$-bimodule and $\mathcal{I} \subset T(\mathcal{E})$ is a graded ideal. We study the geometry of the functor $\Gamma_{n}$ of flat families of truncated $\mathcal{B}=T(\mathcal{E})/\mathcal{I}$-point modules of length $n+1$. We then use the results of our study to show that the point modules over $\mathcal{B}$ are parameterized by the closed points of ${\mathbb{P}}_{X^{2}}(\mathcal{E})$. When $X={\mathbb{P}}^{1}$, we construct, for any $\mathcal{B}$-point module, a graded ${\mathcal{O}}_{X}-\mathcal{B}$-bimodule resolution.

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