Residual intersection theory with reducible schemes

Georg Hein

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2001-18, 9 pages

MSC 2000

14C17 Intersection theory, characteristic classes, intersection multiplicities
14N10 Enumerative problems (combinatorial problems)

We develop a formula (Theorem 5.1) which allows to compute top Chern classes of vector bundles on the vanishing locus V(s) of a section of this bundle. This formula particularly applies in the case when V(s) is the union of locally complete intersections giving the individual contribution of each component and their mutual intersections. We conclude with applications to the enumeration of rational curves in complete intersections in projective space.

Keywords:Residual intersection, reducible cycle, counting rational curves

9 pages