The regularity of points in multi-projective spaces
Abstract
Let I = p_1^{m_1} \cap ... \cap p_s^{m_s} be the defining ideal of a scheme
of fat points in P^{n_1} x ... x P^{n_k} with support in generic position. When
all the m_i's are 1, we explicitly calculate the Castelnuovo-Mumford regularity
of I. In general, if at least one m_i >= 2, we give an upper bound for the
regularity of I, which extends the result of Catalisano, Trung and Valla to the
multi-projective case.