Abbiamo studiato gli elementi generici degli spazi di moduli $\mathfrak{M}_{\mathbb{P}^{2}}(2, c_{1}, c_{2})$ dei fibrati vettoriali stabili di rango 2 su $\mathbb{P}^{2}$ e le loro risoluzioni libere minimali. Ne segue una dimostrazione piuttosto semplice dell'irriducibilità di $\mathfrak{M}_{\mathbb{P}^{2}}(2, c_{1}, c_{2})$.
Referenze Bibliografiche
[Bar77a]
W. BARTH,
Moduli of vector bundles on the projective plane,
Invent. Math. (
1977), no.
42, 63-91. |
MR 460330 |
Zbl 0386.14005[Bar77b]
W. BARTH,
Some properties of stable rank 2 vector bundles on $\mathbb{P}^n$,
Math. Ann. (
1977), no.
226, 125-150. |
MR 429896 |
Zbl 0332.32021[BH78]
W. BARTH-
K. HULEK,
Monads and moduli of vector bundles,
Manuscripta Math. (
1978), no.
25, 323-347. |
MR 509589 |
Zbl 0395.14007[BS92]
G. BOHNHORST and
H. SPINDLER,
The stability of certain vector bundles on Pn,
Lecture Notes (
1992), no.
1507, 39-50. |
MR 1178718 |
Zbl 0773.14008[Dio00] C. DIONISI, Multidimensional matrices and minimal resolutions of vector bundles, Ph.D. thesis, Dip. Matematica «R.Caccioppoli», Università di Napoli, 2000.
[EF80]
G. ELENCWAJG-
O. FORSTER,
Bounding cohomology groups and vector bundles on $\mathbb{P}^n$,
Math. Ann. (
1980), no.
246, 251-270. |
MR 563404 |
Zbl 0432.14011[Ell83]
G. ELLINGSRUD,
Sur l'irréducibilité du module des fibrès stable sur $\mathbb{P}^2$,
Math. Z. (
1983), no.
182, 189-192. |
MR 689296 |
Zbl 0526.14003[Gre89]
M. L. GREEN,
Koszul cohomology and geometry,
Proceedings of the first college on Riemann surfaces held in Trieste (Italy) (M. Cornalba et al., eds.),
World Scientific Publishing Co., November
1989, pp. 177-200. |
MR 1082354 |
Zbl 0800.14004[Har78]
R. HARTSHORNE,
Stable vector bundles of rank 2 on $\mathbb{P}^3$,
Math. Ann.,
238 (
1978), 229-280. |
MR 514430 |
Zbl 0411.14002[Har83]
R. HARTSHORNE,
Algebraic geometry,
Graduate Texts in Mathematics, no.
52,
Springer-Verlag, New York-Heidelberg-Berlin,
1983. |
MR 463157 |
Zbl 0531.14001[HL93]
A. HIRSCHOWITZ-
Y. LASZLO,
Fibrés génériques sur le plan projectif,
Math. Ann. (
1993), no.
297, 85-102. |
MR 1238408 |
Zbl 0808.14007[Hor64]
G. HORROCKS,
Vector bundles on the punctured spectrum of a local ring,
Proc. Lond. Math. Soc., III. Ser.,
14 (
1964), 689-713. |
MR 169877 |
Zbl 0126.16801[Hor87]
G. HORROCKS,
Vector bundles on the punctured spectrum of a local ring II,
Vector bundles on algebraic varieties,
Stud. Math., no.
11,
Tata Inst. Fundam. Res.,
1987, Bombay 1984, pp. 207-216. |
MR 893599 |
Zbl 0677.14001[Hul79]
K. HULEK,
Stable rank $2$ vector bundles on $\mathbb{P}^2$ with $c_2$ odd,
Math. Ann. (
1979), no.
242, 241-266. |
MR 545217 |
Zbl 0407.32013[Hul80]
K. HULEK,
On the classification of stable rank-$k$ vector bundles over the projective plane, A. Hirschowitz (ed):
Vector bundles and differential equations,
Progress in Mathematics, no.
7,
Birkhäuser, Boston-Basel-Stuttgart,
1980, Nice 1979, pp. 113-144. |
MR 589223 |
Zbl 0446.14006[Mag99] M. MAGGESI, Some results on holomorphic vector bundles over projective spaces, Ph.D. thesis, Dip. Matematica «U. Dini» , Università di Firenze, 1999.
[OSS80]
C. OKONEK-
M. SCHNEIDER-
H. SPINDLER,
Vector bundles on complex projective spaces,
Progress in Mathematics, no.
3,
Birkhäuser, Boston-Basel-Stuttgart,
1980. |
MR 561910 |
Zbl 0438.32016[Pot79]
J. LE POTIER,
Fibrés stables de rang $2$ sur $\mathbb{P}^2$,
Math. Ann. (
1979), no.
241, 217-256. |
MR 535556 |
Zbl 0405.14008[Sch61]
R. L. E. SCHWARZENBERGER,
Vector bundles on the projective plane,
Proc. London Math. Soc., 3 (
1961), no.
11, 623-640. |
MR 137712 |
Zbl 0212.26004