Families of low dimensional determinantal schemes


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Series/Report no

Journal of Pure and Applied Algebra;215 (7)



Document type


A scheme X in P^n of codimension c is called standard determinantal if its homogeneous saturated ideal can be generated by the t x t minors of a homogeneous t x (t+c-1) matrix (f_{ij}). Given integers a_0 <= a_1 <= ... <= a_{t+c-2} and b_1 <= ... <= b_t, we denote by W_s(b;a) the stratum of Hilb(P^n) of standard determinantal schemes where f_{ij} are homogeneous polynomials of degrees a_j-b_i and Hilb(P^n) is the Hilbert scheme (if n-c > 0, resp. the postulation Hilbert scheme if n-c = 0). Focusing mainly on zero and one dimensional determinantal schemes we determine the codimension of W_s(b;a) in Hilb(P^n) and we show that Hilb(P^n) is generically smooth along W_s(b;a) under certain conditions. For zero dimensional schemes (only) we find a counterexample to the conjectured value of W_s(b;a) appearing in Kleppe and Miro-Roig [25].



Postprint version of published article. Original available at URL: http://dx.doi.org/10.1016/j.jpaa.2010.10.007

Permanent URL (for citation purposes)

  • http://hdl.handle.net/10642/600