Timeline for Can any simplicial toric variety be embedded in a product of projective spaces?
Current License: CC BY-SA 3.0
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| Jan 22, 2018 at 11:13 | comment | added | Mtheorist | @byu In that case, could we instead show that $(\mathbb{C}^N\backslash U/(\mathbb{C^*})^m)$ is isomorphic to a product of $m$ spaces (not necessarily projective) with Picard number 1, or a hypersurface thereof? | |
| Nov 15, 2017 at 6:55 | vote | accept | Mtheorist | ||
| Nov 14, 2017 at 19:16 | answer | added | Tippi | timeline score: 6 | |
| Nov 14, 2017 at 17:24 | comment | added | byu | No, such hypersurfaces would have Picard number equal to $m$, but there are many simplicial toric varieties (e.g., weighted projective spaces), which have Picard number 1 (but are not hypersurfaces). In fact, most of the threefolds $P(O+O(a)+O(b))$ (over $P^1$, for $a,b$ integers) cannot be embedded in a product of two projective spaces. | |
| Nov 14, 2017 at 16:25 | history | edited | Mtheorist | CC BY-SA 3.0 |
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| Nov 14, 2017 at 16:13 | history | asked | Mtheorist | CC BY-SA 3.0 |