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Projective quadric cone with one singular vertex

Over an algebraically closed field of characteristic other than two, the rank-

r + 1

quadric

V (X_{0}^{2} + \dots + X_{r}^{2}) \subseteq P^{r + 1}

is an irreducible

r

-dimensional cone for

r \geq 2

, and its singular locus is the omitted-coordinate vertex

[0 : \dots : 0 : 1]

.

Table of contents 97 1
- Projective variety with a prescribed-dimensional singular locus Projective quadric cone with one singular vertex 62

 Ancestors (6)