Singularities of the curvilinear Hilbert scheme of hypersurfaces

이화영; 김호성

doi:10.4134/BKMS.b240451

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Singularities of the curvilinear Hilbert scheme of hypersurfaces

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singularity Hilbert scheme

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초록

Let $Y\subset \mathbb P^n$ be a general hypersurface of degree $d$ and let ${\bf a}=(a_1,\ldots,a_r)$ be a sequence of positive integers with $\sum a_i=d$. In this paper we study the singularities of the curvilinear Hilbert scheme $S_{\bf a }(Y)$ of points on $Y$ with multiplicity $\mathbf a$ (see Definition \ref{d.relHilb}).

Abstract

Let $Y\subset \mathbb P^n$ be a general hypersurface of degree $d$ and let ${\bf a}=(a_1,\ldots,a_r)$ be a sequence of positive integers with $\sum a_i=d$. In this paper we study the singularities of the curvilinear Hilbert scheme $S_{\bf a }(Y)$ of points on $Y$ with multiplicity $\mathbf a$ (see Definition \ref{d.relHilb}).

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