Degrees of High-dimensional Subvarieties of Determinantal Varieties
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چکیده
Let n = pab, where p is a prime, and g.c.d.(p, b) = 1. In Pn −1, let Xr be the variety defined by rank((xi,j)) ≤ n − r. We show that any subvariety of Xr of codimension less than par must have degree a multiple of p. We also show that the bounds on the codimension in our results are strict by exhibiting subvarieties of the appropriate codimension whose degrees are
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تاریخ انتشار 2005