UC Irvine

The Thom-Porteous formula allows one to compute the cohomology class of a degeneracy locus of maps between vector bundles, given that certain codimension conditions are satisfied. It is known that the Hilbert scheme on projective space may be expressed as a degeneracy locus in a Grassmannian, and in a similar fashion, so can the Quot scheme. Here we determine cases in which the expected codimension agrees with the actual codimension and evaluate the cohomology class. We also give exact conditions for the existence of isotropic subspaces of Schur modules.