Sia una curva irriducibile nodale di genere aritmetico . In queste note vogliamo mostrare come il sistema lineare delle quadriche, contenenti un opportuno modello proiettivo della curva, permette di descrivere i fibrati vettoriali semistabili, di rango , su .
@article{BUMI_1998_8_1B_3_611_0,
author = {Sonia Brivio},
title = {On rank $2$ semistable vector bundles over an irreducible nodal curve of genus $2$},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {1-A},
year = {1998},
pages = {611-629},
zbl = {0934.14021},
mrnumber = {1662337},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_1998_8_1B_3_611_0}
}
Brivio, Sonia. On rank $2$ semistable vector bundles over an irreducible nodal curve of genus $2$. Bollettino dell'Unione Matematica Italiana, Tome 1-A (1998) pp. 611-629. http://gdmltest.u-ga.fr/item/BUMI_1998_8_1B_3_611_0/
[A] , Compactified Jacobians, Preprint (1996).
[AT] , Vector bundles over an elliptic curve, Proc. London Math. Soc., 7 (1957), 414-452. | MR 131423 | Zbl 0084.17305
[A-C-G-H] ---, Geometry of Algebraic Curves, I, Springer, Berlin (1985). | Zbl 0559.14017
[Ba] , Stable curves, Lectures on Riemann surfaces, Proc. of College at I.C.T.P.Trieste (1987).
[BE] , Moduli of rank two vector bundles, theta divisors, and the geometry of curves in projective spaces, J. Diff. Geom., 35 (1992), 429-469. | MR 1158344 | Zbl 0787.14014
[B-V] -, The theta divisor of is very ample if is not hyperelliptic, Duke Math. J., 82, 3 (1996), 503-552. | MR 1387683 | Zbl 0876.14024
[C] , Pluricanonical-Gorenstein curves, Enumarative Geometry and Classical Algebraic Geometry, Nice, Prog. in Math., Birkhäuser, 24 (1981), 51-95. | MR 685764 | Zbl 0518.14017
[C-F] -, Divisor of small genus on algebraic surfaces and projective embeddings, Israel Mathematical Conference Proc. | Zbl 0855.14004
[C-F-H-R] ---, Embeddings of curves and surfaces, Preprint (1996). | Zbl 0933.14003
[D] , Compactification of generalized Jacobian, Proc. Indian Acad. Sci. Sect. Math. Sci., 88 (1979), 419-457. | MR 569548 | Zbl 0442.14016
[E-H] -, On varieties of minimal degree, (A centennial account), Algebraic Geometry, Proceeding of Symposia in Pure Mathematics, 46 (1987), 3-13. | MR 927946 | Zbl 0646.14036
[G-H] -, Principles of Algebraic Geometry, Wiley, New-York (1978). | MR 507725 | Zbl 0408.14001
[H] , Algebraic Geometry, Springer, Berlin (1977). | MR 463157 | Zbl 0367.14001
[M] , On the equations defining Abelian Varieties, Invent. Math., 1 (1966), 287-354. | MR 204427 | Zbl 0219.14024
[N] , Lectures on Introduction to Moduli Problems and Orbit Spaces, Tata Institute of Fundamental Research, Bombay (1978). | MR 546290 | Zbl 0411.14003
[N-R1] -, Moduli of vector bundles on a compact Riemann surface, Ann. Math., 89 (1969), 19-51. | MR 242185 | Zbl 0186.54902
[N-R2] -, 2-theta linear systems on Abelian Varieties, Vector Bundles on Algebraic Varieties, Oxford (1989), 415-427. | MR 893605 | Zbl 0685.14023
[S1] , Space of unitary vector bundles on a compact Riemann surface, Ann. Math., 85 (1967), 303-336. | MR 233371 | Zbl 0173.23001
[S2] , Fibres Vectoriels sur les courbes algebriques, Asterisque, 96 (1982). | MR 699278 | Zbl 0517.14008