Theta divisors and the geometry of tautological model

• Autores: Sonia Brivio
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 1, 2018, págs. 131-150
• Idioma: inglés
• DOI: 10.1007/s13348-017-0198-2
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• Resumen

  • Let E be a stable vector bundle of rank r and slope 2g-1 on a smooth irreducible complex projective curve C of genus g \ge 3. In this paper we show a relation between theta divisor \Theta _E and the geometry of the tautological model P_E of E. In particular, we prove that for r > g-1, if C is a Petri curve and E is general in its moduli space then \Theta _E defines an irreducible component of the variety parametrizing (g-2)-linear spaces which are g-secant to the tautological model P_E. Conversely, for a stable, (g-2)-very ample vector bundle E, the existence of an irreducible non special component of dimension g-1 of the above variety implies that E admits theta divisor.