Equal-degree dimension conjecture for good determinantal schemes

Let W(0;d)W(\underline{0};\underline{d}) be the locus of good determinantal schemes in Pn+c\mathbb{P}^{n+c} of codimension cc given by the maximal minors of a t×(t+c1)t\times(t+c-1) matrix whose entries are homogeneous forms of degree dd. Equal-degree dimension conjecture. Then

dimW(0;d)=t(t+c1)(d+n+cn+c)t2(t+c1)2+1.\dim W(\underline{0};\underline{d})=t(t+c-1)\binom{d+n+c}{n+c}-t^2-(t+c-1)^2+1.

This is presented as a more precise special case that the authors would like to establish, namely the equal-degree case of the preceding dimension conjecture. Its status is not resolved in the supplied text.

Sources & referencesView supporting material

Primary source

Jan O. Kleppe and Rosa M. Miro-Roig, “Dimension of Families of Determinantal Schemes”, arXiv:math/0209011 (2002).

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