Subschemes of the Border Basis Scheme
Người báo cáo: Martin Kreuzer ( Universität Passau)

Thời gian: 9h, Thứ tư 20/9/2017.
Địa điểm: P6, Nhà A14, Viện Toán học, 18 Hoàng Quốc Việt, Hà Nội
Tóm tắt: 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.

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