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arXiv · 2403.03146

Unexpected but recurrent phenomena for Quot and Hilbert schemes of points

Franco Giovenzana·Luca Giovenzana·Michele Graffeo·Paolo Lella
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Abstract

We investigate some aspects of the geometry of two classical generalisations of the Hilbert schemes of points. Precisely, we show that parity conjecture for $\text{Quot}_r^d\mathbb{A}^3$ already fails for $d=8$ and $r=2$ and that lots of the elementary components of the nested Hilbert schemes of points on smooth quasi-projective varieties of dimension at least 4 are generically non-reduced. We also deduce that nested Hilbert schemes of points on smooth surfaces have generically non-reduced components. Finally, we give an infinite family of elementary components of the classical Hilbert schemes of points.

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Franco Giovenzana, Luca Giovenzana, Michele Graffeo, Paolo Lella. 2024-06-21. Unexpected but recurrent phenomena for Quot and Hilbert schemes of points. https://arxiv.org/abs/2403.03146

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