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Marked bases and Hilbert schemes of points

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EMGW02 - Applied and computational algebraic geometry

Marked bases are special sets of generators of polynomial ideals. I will begin by comparing marked bases with other type of generators (Gröbner/border bases) focusing on computational aspects and on the study of deformations of ideals. In the second part of the talk, I will explain how to use marked bases for studying the Hilbert scheme of points. In particular, I will discuss the construction of counterexamples to the so-called “Parity conjecure” which states that the dimension of the tangent space to the Hilbert scheme of d points in the affine 3-space has (at any point) the same parity of d. The construction of the counterexamples is a joint result with Luca Giovenzana, Franco Giovenzana and Michele Graffeo.

This talk is part of the Isaac Newton Institute Seminar Series series.

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