Unexpected but recurrent phenomena for Quot and Hilbert schemes of points

Autor:	Giovenzana, Franco, Giovenzana, Luca, Graffeo, Michele, Lella, Paolo
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra 14C05 13D10 13F55 13P10
Druh dokumentu:	Working Paper
Popis:	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. Comment: Added a statement proving that the nested Hilbert scheme of a smooth surface admits generically non-reduced components. Final version, to appear in Rend. Sem. Mat. Univ. Politec. Torino
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.03146 Zobrazit plný text záznamu View this record from Arxiv