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arXiv · 2203.16068

Euler-symmetric complete intersection in projective space

Zhijun Luo
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Abstract

Euler-symmetric projective varieties, introduced by Baohua Fu and Jun-Muk Hwang in 2020, are nondegenerate projective varieties admitting many $\mathbb{C}^{\times}$-actions of Euler type. They are quasi-homogeneous and uniquely determined by their fundamental forms at a general point. In this paper, we study complete intersections in projective spaces which are Euler-symmetric. It is proven that such varieties are complete intersections of hyperquadrics and the base locus of the second fundamental form at a general point is again a complete intersection.

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Zhijun Luo. 2022-03-30. Euler-symmetric complete intersection in projective space. https://doi.org/10.1016/j.jalgebra.2023.02.026

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