A counterexample to the parity conjecture

Autor:	Giovenzana, Franco, Giovenzana, Luca, Graffeo, Michele, Lella, Paolo
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra 14C05 (Primary) 13D10 13F55 13P10 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Let $[Z]\in\text{Hilb}^d \mathbb A^3$ be a zero-dimensional subscheme of the affine three-dimensional complex space of length $d>0$. Okounkov and Pandharipande have conjectured that the dimension of the tangent space of $\text{Hilb}^d \mathbb A^3$ at $[Z]$ and $d$ have the same parity. The conjecture was proven by Maulik, Nekrasov, Okounkov and Pandharipande for points $[Z]$ defined by monomial ideals and very recently by Ramkumar and Sammartano for homogeneous ideals. In this paper we exhibit a family of zero-dimensional schemes in $\text{Hilb}^{12} \mathbb A^3$, which disproves the conjecture in the general non-homogeneous case. Comment: 13 pages. Final version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.18191 Zobrazit plný text záznamu View this record from Arxiv