A Linear Bound for Frobenius Powers and an Inclusion Bound for Tight Closure
نویسنده
چکیده
Let I denote an R+-primary homogeneous ideal in a normal standard-graded Cohen-Macaulay domain over a field of positive characteristic p. We give a linear degree bound for the Frobenius powers I [q] of I, q = p, in terms of the minimal slope of the top-dimensional syzygy bundle on the projective variety ProjR. This provides an inclusion bound for tight closure. In the same manner we give a linear bound for the Castelnuovo-Mumford regularity of the Frobenius powers I . Mathematical Subject Classification (2000): 13A35; 13D02; 14J60
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