Timeline for When is a toric variety a Poincare duality space?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2021 at 14:54 | comment | added | Evgeny Shinder | Philip Engel: most likely PD won't hold in this case. E.g. for threefolds you have 4 rays in maximal cones, and I think $H_2(X)$ and $H_4(X)$ will typically have different dimensions. One way to approach this is to subdivide the cones to make an orbifold resolution $X' \to X$ and compare homology of $X$ and of $X'$. | |
| Feb 27, 2021 at 14:02 | comment | added | Philip Engel | The example I was thinking about was not simplicial, but is very close: The number of generators of any maximal cone exceeds the dimension by exactly 1. | |
| Feb 27, 2021 at 13:52 | comment | added | Philip Engel | Thanks for the question, I only wanted PD rationally. | |
| Feb 26, 2021 at 23:14 | comment | added | Evgeny Shinder | Not sure from the question if you want integrally or rationally? An easy condition is that if for every cone in the fan the rays are linearly independent (I think such cones are called simplicial), then the toric variety has quotient singularities and Poincare duality holds rationally. | |
| Feb 26, 2021 at 22:54 | history | asked | Philip Engel | CC BY-SA 4.0 |