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# Degeneracy of 2-Forms and 3-Forms

Published:2005-12-01
Printed: Dec 2005
• L. M. Fehér
• A. Némethi
• R. Rimányi
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## Abstract

We study some global aspects of differential complex 2-forms and 3-forms on complex manifolds. We compute the cohomology classes represented by the sets of points on a manifold where such a form degenerates in various senses, together with other similar cohomological obstructions. Based on these results and a formula for projective representations, we calculate the degree of the projectivization of certain orbits of the representation $\Lambda^k\C^n$.
 Keywords: Classes of degeneracy loci, 2-forms, 3-forms, Thom polynomials, global singularity theory
 MSC Classifications: 14N10 - Enumerative problems (combinatorial problems) 57R45 - Singularities of differentiable mappings