Determinantal varieties from point configurations on hypersurfaces

Autor:	Caminata, Alessio, Moon, Han-Bom, Schaffler, Luca
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra 14M12 14N20 14J70 14J17 13C40
Druh dokumentu:	Working Paper
Popis:	We consider the scheme $X_{r,d,n}$ parametrizing $n$ ordered points in projective space $\mathbb{P}^r$ that lie on a common hypersurface of degree $d$. We show that this scheme has a determinantal structure and we prove that it is irreducible, Cohen-Macaulay, and normal. Moreover, we give an algebraic and geometric description of the singular locus of $X_{r,d,n}$ in terms of Castelnuovo-Mumford regularity and $d$-normality. This yields a characterization of the singular locus of $X_{2,d,n}$ and $X_{3,2,n}$. Comment: 24 pages. Final version with minor corrections. To appear in International Mathematics Research Notices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.13177 Zobrazit plný text záznamu View this record from Arxiv