Quasi-lines and their degenerations
Laurent Bonavero; Andreas Höring
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)
- Volume: 6, Issue: 3, page 359-383
- ISSN: 0391-173X
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topBonavero, Laurent, and Höring, Andreas. "Quasi-lines and their degenerations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.3 (2007): 359-383. <http://eudml.org/doc/272270>.
@article{Bonavero2007,
abstract = {In this paper we study the structure of manifolds that contain a quasi-line and give some evidence towards the fact that the irreducible components of degenerations of the quasi-line should determine the Mori cone. We show that the minimality with respect to a quasi-line yields strong restrictions on fibre space structures of the manifold.},
author = {Bonavero, Laurent, Höring, Andreas},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {359-383},
publisher = {Scuola Normale Superiore, Pisa},
title = {Quasi-lines and their degenerations},
url = {http://eudml.org/doc/272270},
volume = {6},
year = {2007},
}
TY - JOUR
AU - Bonavero, Laurent
AU - Höring, Andreas
TI - Quasi-lines and their degenerations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2007
PB - Scuola Normale Superiore, Pisa
VL - 6
IS - 3
SP - 359
EP - 383
AB - In this paper we study the structure of manifolds that contain a quasi-line and give some evidence towards the fact that the irreducible components of degenerations of the quasi-line should determine the Mori cone. We show that the minimality with respect to a quasi-line yields strong restrictions on fibre space structures of the manifold.
LA - eng
UR - http://eudml.org/doc/272270
ER -
References
top- [1] T. Ando, On extremal rays of the higher-dimensional varieties, Invent. Math.81 (1985), 347–357. Zbl0554.14001MR799271
- [2] V. Ancona, T. Peternell and J. A. Wiśniewski, Fano bundles and splitting theorems on projective spaces and quadrics, Pacific J. Math.163 (1994), 17–42. Zbl0808.14013MR1256175
- [3] L. B ădescu, M. C. Beltrametti and P. Ionescu, Almost-lines and quasi-lines on projective manifolds, In: “Complex analysis and algebraic geometry”, de Gruyter, Berlin, 2000, 1–27. Zbl1078.14010MR1760869
- [4] K. Cho, Y. Miyaoka and N. I. Shepherd-Barron, Characterizations of projective space and applications to complex symplectic manifolds, In: “Higher dimensional birational geometry” (Kyoto, 1997), Adv. Stud. Pure Math., Vol. 35, Math. Soc. Japan, Tokyo, 2002, 1–88. Zbl1063.14065MR1929792
- [5] O. Debarre, “Higher-Dimensional Algebraic Geometry”, Universitext, Springer-Verlag, New York, 2001. Zbl0978.14001MR1841091
- [6] T. Fujita, On polarized manifolds whose adjoint bundles are not semipositive, In: “Algebraic geometry” (Sendai, 1985), Adv. Stud. Pure Math., Vol. 10, North-Holland, Amsterdam, 1987, 167–178. Zbl0659.14002MR946238
- [7] R. Hartshorne, Varieties of small codimension in projective space, Bull. Amer. Math. Soc.80 (1974), 1017–1032. Zbl0304.14005MR384816
- [8] R. Hartshorne, “Algebraic Geometry”, Graduate Texts in Mathematics, Vol. 52. Springer-Verlag, New York, 1977. Zbl0367.14001MR463157
- [9] R. Hartshorne, Stable vector bundles of rank on , Math. Ann.238 (1978), 229–280. Zbl0411.14002MR514430
- [10] N. J. Hitchin, Kählerian twistor spaces, Proc. London Math. Soc.43 (1981), 133–150. Zbl0474.14024MR623721
- [11] P. Ionescu and D. Naie, Rationality properties of manifolds containing quasi-lines, Internat. J. Math.14 (2003), 1053–1080. Zbl1080.14512MR2031183
- [12] P. Ionescu and C. Voica, Models of rationally connected manifolds, J. Math. Soc. Japan55 (2003), 143–164. Zbl1084.14052MR1939190
- [13] S. Kebekus, Characterizing the projective space after Cho, Miyaoka and Shepherd-Barron, In: “Complex geometry” (Göttingen, 2000), Springer, Berlin, 2002, 147–155. Zbl1046.14028MR1922103
- [14] Kawamata, Yujiro, Matsuda, Katsumi and Matsuki, Kenji, Introduction to the minimal model problem, In: “Algebraic Geometry” (Sendai, 1985), Adv. Stud. Pure Math., Vol. 10, North-Holland, Amsterdam, 1987, 283–360. Zbl0672.14006MR946243
- [15] J. Kollár, “Rational Curves on Algebraic Varieties”, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics, Vol. 32, Springer-Verlag, Berlin, 1996. Zbl0877.14012MR1440180
- [16] S. Mori and S. Mukai, Classification of Fano -folds with , Manuscripta Math. 36 (1981/82), 147–162. Zbl0478.14033MR641971
- [17] S. Mori and S. Mukai, On Fano -folds with , In: “Algebraic varieties and analytic varieties” (Tokyo, 1981), Adv. Stud. Pure Math. Vol. 1, North-Holland, Amsterdam, 1983, 101–129. Zbl0537.14026MR715648
- [18] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math.116 (1982), 133–176. Zbl0557.14021MR662120
- [19] C. Okonek, M. Schneider and H. Spindler, “Vector Bundles on Complex Projective Spaces”, Progress in Mathematics, Vol. 3, Birkhäuser Boston, Mass., 1980. Zbl0438.32016MR561910
- [20] W. M. Oxbury, Twistor spaces and Fano threefolds, Quart. J. Math. Oxford Ser.45 (1994), 343–366. Zbl0817.14019MR1295581
- [21] M. Szurek and J. A. Wiśniewski, Fano bundles over and , Pacific J. Math.141 (1990), 197–208. Zbl0705.14016MR1028270
- [22] M. Szurek and J. A. Wiśniewski, On Fano manifolds, which are -bundles over , Nagoya Math. J.120 (1990), 89–101. Zbl0728.14037MR1086572
- [23] J. A. Wiśniewski, On contractions of extremal rays of Fano manifolds, J. Reine Angew. Math.417 (1991), 141–157. Zbl0721.14023MR1103910
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