Abstract We construct wonderful compactifications of the spaces linear maps and symmetric a given rank as blowups secant varieties Segre Veronese varieties. Furthermore, we investigate their birational geometry relations with some degree two stable maps.

We consider various aspects of the Segre variety S := S1,1,1(2) in PG(7, 2), whose stabilizer group GS < GL(8, 2) has the structure N o Sym(3), where N := GL(2, 2) × GL(2, 2) × GL(2, 2). In particular we prove that S determines a distinguished Z3-subgroup Z < GL(8, 2) such that AZA−1 = Z, for all A ∈ GS , and in consequence S determines a GS invariant spread of 85 lines in PG(7, 2). Furthermore...

We prove a base point freeness result for linear systems of forms vanishing at general double points the projective plane. For tensors we study uniqueness problem representation tensor as sum terms corresponding to and tangent vectors Segre variety associated with format tensor. give complete results unions one vector.