Osculating varieties and their joins: \(\mathbb{P}^1\times \mathbb{P}^1\)





Let \(X\subset \mathbb{P}^r\) be an integral projective variety. We study the dimensions of the joins of several copies of the osculating varieties \(J(X,m)\) of \(X\). Our methods are general, but we give a full description in all cases only if \(X\) is a linearly normal embedding of \(\mathbb{P}^1\times \mathbb{P}^1\). For these embeddings of \(\mathbb{P}^1\times \mathbb{P}^1\) we give several examples and then study the joins of one copy of \(J(X,m)\) and an arbitrary number of copies of \(X\).


Osculating space , joins of projective varieties , secant varieties , quadric surface

Mathematics Subject Classification:

14N07 , 14N05
  • Pages: 331–347
  • Date Published: 2023-08-28
  • Vol. 25 No. 2 (2023)

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How to Cite

E. Ballico, “Osculating varieties and their joins: \(\mathbb{P}^1\times \mathbb{P}^1\)”, CUBO, pp. 331–347, Aug. 2023.