Euler-symmetric complete intersection in projective space
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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- 10.48550/arXiv.2203.16068
- arXiv:
- arXiv:2203.16068
- Bibcode:
- 2022arXiv220316068L
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- doi:10.1016/j.jalgebra.2023.02.026