Deformation and Unobstructedness of Determinantal Schemes

Deformation and Unobstructedness of Determinantal Schemes Synopsis

"A closed subscheme X [is a proper subset of] Pn is said to be determinantal if its homogeneous saturated ideal can be generated by the s [times] s minors of a homogeneous p [times] q matrix satisfying (p [minus] s [plus] 1)(q [minus] s [plus] 1) [equals] n [minus] dimX and it is said to be standard determinantal if, in addition, s [equals] min(p, q). Given integers a1 [leq] a2 [leq] [dots] [leq] at[plus]c[minus]1 and b1 [leq] b2 [leq] [dots] [leq] bt we consider t [times] (t [plus] c [minus] 1) matrices A [equals] (fij) with entries homogeneous forms of degree aj [minus] bi and we denote by W(b; a; r) the closure of the locus W(b; a; r) [is a proper subset of] Hilbp(t)(Pn) of determinantal schemes defined by the vanishing of the (t[minus]r[plus]1)[times](t[minus]r[plus]1) minors of such A for max{1, 2[minus]c} [leq] r [less than] t. W(b; a; r) is an irreducible algebraic set. First of all, we compute an upper r-independent bound for th

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