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 > 2. In this paper we show a relation between theta divisor associated to E and the geometry of the tautological model 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, its theta divisor defines an irreducible component of the variety parametrizing (g-2)-linear spaces which are g-secant the tautological model of 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

Brivio, S. (2018). Theta divisors and the geometry of tautological model. COLLECTANEA MATHEMATICA, 69(1), 131-150 [10.1007/s13348-017-0198-2].

Theta divisors and the geometry of tautological model.

Brivio, S
2018

Abstract

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 > 2. In this paper we show a relation between theta divisor associated to E and the geometry of the tautological model 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, its theta divisor defines an irreducible component of the variety parametrizing (g-2)-linear spaces which are g-secant the tautological model of 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
Articolo in rivista - Articolo scientifico
Vector bundles; Theta divisors; Moduli spaces; Tautological map.
English
131
150
20
Published online: 16 may 2017
Brivio, S. (2018). Theta divisors and the geometry of tautological model. COLLECTANEA MATHEMATICA, 69(1), 131-150 [10.1007/s13348-017-0198-2].
Brivio, S
File in questo prodotto:
File Dimensione Formato  
Collectanea.pdf

Solo gestori archivio

Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Dimensione 513.2 kB
Formato Adobe PDF
513.2 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/154686
Citazioni
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
Social impact