Pieri-type intersection formulas and primary obstructions for decomposing $2$-forms
Volume 87 / 2001
Colloquium Mathematicum 87 (2001), 201-210
MSC: Primary 14M15; Secondary 14M17, 14N10.
DOI: 10.4064/cm87-2-6
Abstract
We study the homological intersection behaviour for the Chern cells of the universal bundle of $G(d,Q_n)$, the space of $[d]$-planes in the smooth quadric $Q_n$ in ${\mathbb P}^{n+1}$ over the field of complex numbers. For this purpose we define some auxiliary cells in terms of which the intersection properties of the Chern cells can be described. This is then applied to obtain some new necessary conditions for the global decomposability of a 2-form of constant rank.
