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.

References in corpus (1)

• Equivariant compactifications of a nilpotent group by $G/P$