Time: 9h, Wednesday, July 8, 2020

Location: Room 612, Building A6, Institutte of Mathematics and GM https://meet.google.com/vha-ujbp-kwo

Abstract: Let X be a 0-dimensional scheme in the affine space A^n_K over an arbitrary field K, let I_X be the defining ideal of X. Then the coordinate ring of X is R=K[x_1,..,x_n]/I_X. The scheme X is called a strict complete intersection if the degree form ideal DF(I_X) is generated by a regular sequence of homogeneous polynomials in K[x_1,...,x_n]. In this talk, we discuss some properties of this special class of 0-dimensional schemes. It is well-known that a strict complete intersection X is also a Cayley-Bacharach scheme, but the converse is not true in general. Using the Kähler differents associated with X, we provide an additional condition for a Cayley-Bacharach scheme to become a strict complete intersection.