Algebra Seminar 

27/02/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
Santiago Zarzuela, Universitat de Barcelona

Arrangements of linear varieties, D-modules and local cohomolgy

Let $A_k^n$ denote the affine space of dimension $n$ over a field $k$ and $X\subset A_k^n$ be an arrangement of linear subvarieties. Set $R=k[x_1,\dots ,x_n]$ and let $I\subset R$ denote an ideal which defines $X$. If $k$ is a field of characteristic zero, the local cohomology modules modules $H_I^r(R)$ are known to have a module structure over the Weyl algebra $A_n(k)$, and one can therefore consider their characteristic cycles, denoted $\mathrm{CC}(H_I^r(R))$ in this talk. In either the real or the complex case, we shall determine the Betti numbers of the complement of the arrangement $X$ in terms of the multiplicities of the local cohomology modules $H_I^r(R)$.

(Joint work with Josep Àlvarez-Montaner and Ricardo García- López)