Hodge type of the exotic cohomology of complete intersections

Abstract

If X⊂ P n is a smooth complete intersection, its cohomology modulo the one of P n is supported in middle dimension. If the complete intersection is singular, it might also carry exotic cohomology beyond the middle dimension. We show that for this exotic cohomology, one can improve the known bound for the Hodge type of its de Rham cohomology. To cite this article: H. Esnault, D. Wan, C. R. Acad. Sci. Paris, Ser. I 336 (2003).