Hilbert functions of schemes of double and reduced points

18 Jun 2019 Carlini Enrico Catalisano Maria Virginia Guardo Elena Van Tuyl Adam

It remains an open problem to classify the Hilbert functions of double points in $\mathbb{P}^2$. Given a valid Hilbert function $H$ of a zero-dimensional scheme in $\mathbb{P}^2$, we show how to construct a set of fat points $Z \subseteq \mathbb{P}^2$ of double and reduced points such that $H_Z$, the Hilbert function of $Z$, is the same as $H$... (read more)

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