Osculating varieties and their joins: ℙ1 × ℙ1

• Autores: Edoardo Ballico
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 2, 2023, págs. 331-347
• Idioma: inglés
• DOI: 10.56754/0719-0646.2502.331
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Sea X ⊂ ℙr una variedad proyectiva entera. Estudiamos la dimensión de las adjunciones de varias copias de las variedades osculantes J(X, m) de X. Nuestros métodos son generales, pero damos una descripción completa en todos los casos solo si X es un embebimiento linealmente normal de ℙ1 × ℙ1. Para estos embebimientos de ℙ1 × ℙ1 damos varios ejemplos y luego estudiamos las adjunciones de una copia de J(X, m) y un número arbitrario de copias de X.

  • English

    Abstract Let X ⊂ ℙr 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 ℙ1 × ℙ1. For these embeddings ℙ1 × ℙ1 we give several examples and then study the joins of one copy of J(X, m) and an arbitrary number of copies of X.

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