Tempered currents and the cohomology of the remote fiber of a real polynomial map
| dc.creator | Braverman, Alexander | |
| dc.creator | Braverman, Maxim | |
| dc.date | 1997-04-02 | |
| dc.date.accessioned | 2026-07-07T09:07:15Z | |
| dc.date.available | 2026-07-07T09:07:15Z | |
| dc.description | Let $p:R^n\to R$ be a polynomial map. Consider the complex $S'Ω^*(\RR^n)$ of tempered currents on $R^n$ with the twisted differential $d_p=d-dp$ where $d$ is the usual exterior differential and $dp$ stands for the exterior multiplication by $dp$. Let $t\in R$ and let $F_t=p^{-1}(t)$. In this paper we prove that the reduced cohomology $\tilda H^k(F_t;C)$ of $F_t$ is isomorphic to $H^{k+1}(S'Ω^*(\RR^n),d_p)$ in the case when $p$ is homogeneous and $t$ is any positive real number. We conjecture that this isomorphism holds for any polynomial $p$, for $t$ large enough (we call the $F_t$ for $t >> 0$ the remote fiber of $p$) and we prove this conjecture for polynomials that satisfy certain technical condition. The result is analogous to that of A. Dimca and M. Saito, who give a similar (algebraic) way to compute the reduced cohomology of the generic fiber of a complex polynomial. | |
| dc.description | LaTeX 2e | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9704001 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9704001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150301 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Tempered currents and the cohomology of the remote fiber of a real polynomial map | |
| dc.type | text |