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will be called a skewform. A subspace W is isotropic for a if the restriction of a to W is null, i.e., a(x, y) =0 for all X, YE W. More generally, if a = b 1 ,..., ak} is a collection of skewforms on V then a subspace W is said to be isotropic for a if it is isotropic for each a,. Note that we could choose to think of the collection a as an alternating bilinear map a: Vx V+ Fk. Given a collection a of k skewforms as above let m(a) be the dimension of the largest isotropic subspace for a. Let d(F, n, k) denote the minimum possible value of m(a) as a ranges over all k-tuples of skewforms on an n-dimensional vector space |
