Cohomological Dimension of Non-Complete Hypersurfaces.
We explain the philosophy behind the computations in [BDP] and place them in a wider conceptual setting. We also outline, for toric varieties, the resulting equivalent approach to some key results in that theory.
We study certain kinds of geometric correspondences between (possibly singular) algebraic varieties and we obtain comparison results regarding natural filtrations on the homology of varieties.
Let be the moduli space of -pointed Riemann surfaces of genus . Denote by the Deligne-Mumford compactification of . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of for any and such that .