On the X-rank with respect to linearly normal curves

• Autores: Edoardo Ballico, Alessandra Bernardi
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 64, Fasc. 2, 2013, págs. 141-154
• Idioma: inglés
• DOI: 10.1007/s13348-011-0058-4
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• Resumen

  • In this paper we study the X-rank of points with respect to smooth linearly normal curves ?⊂ℙ? of genus g and degree n+g. We prove that, for such a curve X, under certain circumstances, the X-rank of a general point of X-border rank equal to s is less or equal than n + 1 − s. In the particular case of g = 2 we give a complete description of the X-rank if n = 3, 4; while if n ≥ 5 we study the X-rank of points belonging to the tangential variety of X.