Timeline for Flatness of Chern classes for flat family of sheaves
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jan 27, 2016 at 13:04 | comment | added | Jason Starr | You might check if Gabber-Liu-Lorenzini have proved something about this; they proved results that sound similar to this. | |
| Jan 27, 2016 at 13:02 | comment | added | Jason Starr | ... Finally, to prove the degeneracy loci of $\mathcal{F}$ are flat over $Q$ (for general choices of global sections of $\mathcal{F}$), you will probably use Eagon-Hochster. | |
| Jan 27, 2016 at 11:28 | comment | added | Jason Starr | There is a reduction to the case that $\mathcal{E}$ is locally free of finite rank using Hilbert's Syzygy Theorem. Also it suffices to prove the result for $\mathcal{E}(m)$ with $m\gg 0$ using the following identity in the K-group of the projective space $\mathbb{P}^n$ in which $X$ embeds: $\sum_r \binom{n+1}{r}(-1)^r[\mathcal{O}(m+r)] = 0$. Also, using Whitney sum, it suffices to prove the result for $\mathcal{F} = \mathcal{E}(m)\oplus \mathcal{O}(m)^{\oplus N}$ for $N\gg 0$. Now use Thom-Porteous. You need to prove, ala Bertini, that degeneracy loci of $\mathcal{F}$ are flat over $Q$. | |
| Jan 26, 2016 at 8:06 | history | asked | user307725 | CC BY-SA 3.0 |