It is shown that an irreducible cubic hypersurface with nonzero Hessian and smooth singular locus is the secant variety of a Severi variety if and only if its Lie algebra of infinitesimal linear automorphisms admits a nonzero prolongation.

中文翻译：

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三次超曲面中严重变异的割线变异的表征

结果表明，具有非零 Hessian 和光滑奇异轨迹的不可约三次超曲面是 Severi 簇的割簇，当且仅当其无穷小线性自同构的李代数允许非零延展。