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GROEBNER BASES AND NONEMBEDDINGS OF SOME FLAG MANIFOLDS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 96 / Issue 3 / June 2014
- Published online by Cambridge University Press:
- 31 March 2014, pp. 338-353
- Print publication:
- June 2014
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- Article
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Groebner bases for the ideals determining mod
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}2$ cohomology of the real flag manifolds 
$F(1,1,n)$ and 
$F(1,2,n)$ are obtained. These are used to compute appropriate Stiefel–Whitney classes in order to establish some new nonembedding and nonimmersion results for the manifolds 
$F(1,2,n)$.
A Hilbert Scheme in Computer Vision
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- Journal:
- Canadian Journal of Mathematics / Volume 65 / Issue 5 / 01 October 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 961-988
- Print publication:
- 01 October 2013
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Multiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Gröbner basis for the multiview ideal of
$n$ generic cameras. As the cameras move, the multiview varieties vary in a family of dimension 
$11n\,-\,15$. This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme.
