Computational aspects of Castelnuovo-Mumford regularity
نویسندگان
چکیده
Let I be a homogeneous ideal of the polynomial ring K[x0, . . . , xn], where K is an arbitrary field. Avoiding the construction of a minimal graded free resolution of I, we provide effective methods for computing the Castelnuovo-Mumford regularity of I that also compute other cohomological invariants of K[x0, . . . , xn]/I. We then apply our methods to the defining ideal I(V) of a projective monomial variety of codimension two V and get an explicit formula for the Castelnuovo-Mumford regularity of V, reg (V), in terms of the reduced Gröbner basis of I(V) with respect to the reverse lexicographic order. As a consequence, we show that reg (V) ≤ degV − 1, where degV is the degree of V, and characterize when equality holds. Mathematics Subject Classification (2000). Primary 13P10; Secondary 13D45, 14M25.
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