ProV Logo
0
Stabilization of the cohomology of thick...
Bhatt, Bhargav...

Free

Stabilization of the cohomology of thickenings by Bhatt, Bhargav ( Author )
Lemonjar Open Access
Australian National University
08-08-2023
For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of vector bundles on the formal completion of ${\mathbb P}^n$ along $X$ can be effectively computed as the cohomology on any sufficiently high thickening $X_t=V({\mathcal I^t})$; the main ingredient here is a positivity result for the normal bundle of $X$. Furthermore, we show that the Kodaira vanishing theorem holds for all thickenings $X_t$ in the same range of cohomological degrees; this extends the known version of Kodaira vanishing on $X$, and the main new ingredient is a version of the Kodaira-Akizuki-Nakano vanishing theorem for $X$, formulated in terms of the cotangent complex.
-
Article
pdf
29.34 KB
English
-
MYR 0.01
-
http://arxiv.org/abs/1605.09492
Share this eBook