Time: 9h00, Wednesday, September 20, 2017
Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: For zero-dimensional polynomial ideals of fixed colength, border basis schemes allow us to parametrize open sets covering the Hilbert scheme. They are given by easily describable, explicit quadratic equations. In this talk we present similarly explicit decriptions of subschemes of the border basis scheme which parametrize zero-dimensional schemes having additional properties.
In particular, we shall look at the Gorenstein locus, the Hilbert functions subschemes, the Cayley-Bacharach locus, and the strict Gorenstein locus.
The construction of explicit equations for these subschemes is based on a new, general definition of Cayley-Bacharach schemes and characterizations of the Gorenstein property and the Cayley-Bacharach property via multiplication matrices.