Stability of cubic 3-folds.
type: Item
instance of: scholarly article
title: Stability of cubic 3-folds.
zbMATH Open document ID: 1048.14020
author: Mutsumi Yokoyama
published in: Tokyo Journal of Mathematics
publication date: 2002-01-01T00:00:00Z
review text: The author classifies the (semi)stable cubic 3-folds according to their singular locus. Precisely he proves that a cubic 3-fold \(X\subset \mathbb{P}^4\) is stable (respectively semistable) if and only if it has only double points of type \(A_n\), \(N\leq 4\) (respectively either it has only double points of type \(D_4\), \(A_n\), \(n\leq 5\) or it is isomorphic to the secant variety of the rational normal curve in \(\mathbb{P}^4)\). The proof is based on the study of some suitable one-parameter subgroups of \(SL(5)\). Moreover the closed orbits of the natural action of SL(5) on \(\text{Sym}^3 \mathbb{C}^5\) give an explicit description of the ``border components'' of a compactification of their moduli space.
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 1799654
reviewed by: Luciana Picco Botta
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1244208939
OpenAlex ID: W1991893387
cites work: Q3953899
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cites work: Stability of projective varieties
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cites work: Degenerations of K3 Surfaces of Degree 4
cites work: Q3568183
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DOI: 10.3836/TJM/1244208939
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description: scientific article; zbMATH DE number 1799654