Classification of conic bundles in 5

R. Braun; G. Ottaviani; M. Schneider; F.-O. Schreyer

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1996)

  • Volume: 23, Issue: 1, page 69-97
  • ISSN: 0391-173X

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Braun, R., et al. "Classification of conic bundles in $\mathbb {P}^5$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 23.1 (1996): 69-97. <http://eudml.org/doc/84227>.

@article{Braun1996,
author = {Braun, R., Ottaviani, G., Schneider, M., Schreyer, F.-O.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {low codimension; bounded degree of log-special 3-folds; conic bundle},
language = {eng},
number = {1},
pages = {69-97},
publisher = {Scuola normale superiore},
title = {Classification of conic bundles in $\mathbb \{P\}^5$},
url = {http://eudml.org/doc/84227},
volume = {23},
year = {1996},
}

TY - JOUR
AU - Braun, R.
AU - Ottaviani, G.
AU - Schneider, M.
AU - Schreyer, F.-O.
TI - Classification of conic bundles in $\mathbb {P}^5$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1996
PB - Scuola normale superiore
VL - 23
IS - 1
SP - 69
EP - 97
LA - eng
KW - low codimension; bounded degree of log-special 3-folds; conic bundle
UR - http://eudml.org/doc/84227
ER -

References

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  1. [ACGH] E. Arbarello - M. Cornalba - P. Griffiths - J. Harris, Geometry of algebraic curves I, Grundlehren der math. Wissenschaften267, Springer, Berlin, 1985. Zbl0559.14017MR770932
  2. [A] A. Aure, On surfaces in projective 4-space, Thesis, Oslo, 1987. 
  3. [BBS] M. Beltrametti - A. Biancofiore - A.J. Sommese, Projective N-folds of log-general type I. Trans. Am. Math. Soc.314 (1989), 825-849. Zbl0702.14037MR1005528
  4. [Be] A. Beauville, Variétés de Prym et Jacobiennes intermédiaires, Ann. Sci. École Norm. Sup., 10 (1977), 309-391. Zbl0368.14018MR472843
  5. [BeSo] M. Beltrametti - A.J. Sommese, New properties of special varieties arising from adjunction theory, J. Math. Soc. Japan43 (1991), 381-412. Zbl0754.14027MR1096439
  6. [Bes] G.M. Besana, On the geometry of conic bundles arising in adjunction theory, Math. Nachr.160 (1993), 223-251. Zbl0808.14014MR1245000
  7. [BOSS] R. Braun - G. Ottaviani - F.O. Schreyer - M. Schneider, Boundedness for non-general type 3-folds in P5. In "Complex Analysis and Geometry", V. Ancona - A. Silva Eds., Plenum Press, 1993, pp. 311-338. Zbl0798.14023MR1211889
  8. [BSS1] M. Beltrametti - M. Schneider - A.J. Sommese, Threefolds of degree 9 and 10 in P 5, Math. Ann. 288 (1990), 613-644. Zbl0723.14033MR1079870
  9. [BSS2] M. Beltrametti - M. Schneider - A.J. Sommese, Threefolds of degree 11 in P5. In: "Complex projective geometry", London Math. Soc. Lecture Note Series 179, 1992, pp. 59-80. Zbl0774.14036MR1201375
  10. [DMS] W. Decker - N. Manolache - F.O. Schreyer, Geometry of the Horrocks bundle on P5. In: "Complex projective geometry", London Math. Soc. Lecture Note Series 179, 1992, pp. 128-148. Zbl0774.14013MR1201379
  11. [E] G. Edelmann, 3-folds in P5 of degree 12, Manuscripta math.82 (1994), 393-406. Zbl0812.14026MR1265008
  12. [EP] G. Ellingsrud - C. Peskine, Sur les surfaces lisses de P4, Invent. Math.95 (1989), 1-11. Zbl0676.14009MR969410
  13. [GP] L. Gruson - C. Peskine, Genre des courbes de l'espace projectif. In: "Algebraic Geometry", Lecture Notes in Math. 687, Springer, Berlin, 1977, pp. 31-59. Zbl0412.14011MR527229
  14. [H] G. Horrocks, Examples of rank three vector bundles on five-dimensional projective space, J. London Math. Soc.18 (1978), 15-27. Zbl0388.14009MR502651
  15. [K] C. Koelblen, Surfaces de P4 tracées sur une hypersurface cubique, J. reine angew. Math.433 (1992), 113-141. Zbl0753.14033MR1191602
  16. [M1] S. Mukai, Curves and symmetric spaces, Proc. Japan Acad. Ser. A Math. Sci.68 (1992), 7-10. Zbl0768.14014MR1158012
  17. [M2] S. Mukai, Fano 3-folds. In: "Complex Projective Geometry", London Math. Soc. Lecture Notes Series 179, 1992, pp. 255-263. Zbl0774.14037MR1201387
  18. [O] G. Ottaviani, 3-folds in P5 which are scrolls, Annali Scuola Norm. Sup. Pisa Cl. Sci., 19 (1992), 451-471. Zbl0786.14026MR1205407
  19. [Sch] M. Schneider, 3-folds in P5: Classification in low degree and finiteness results. In: "Geometry of complex projective varieties", Cetraro 1990, A. Lanteri - M. Palleschi - D. Struppa Eds., Mediterranean Press, Rende, 1993, pp. 275-288. Zbl0939.14018MR1225600
  20. [S1] A.J. Sommese, Hyperplane sections of projective surfaces I. The adjunction mapping. Duke Math. J.46 (1979), 377-401. Zbl0415.14019MR534057
  21. [S2] A.J. Sommese, Hyperplane sections. Proc. of the Algebraic Geometry conference, Univ. of Illinois at Chicago Circle, 1980, Lecture Notes in Math. 862, Springer-Verlag, Berlin, 1981, pp. 232-271. Zbl0494.14001MR644822
  22. [S3] A.J. Sommese, On the adjunction theoretic structure of projective varieties, Complex Analysis and Algebraic Geometry, Proceedings Göttingen 1985, Lecture Notes in Math. 1194, Springer, Berlin, 1986, pp. 175-213. Zbl0601.14029MR855885
  23. [SV] A.J. Sommese - A. Van De Ven, On the adjunction mapping, Math. Ann.278 (1987), 593-603. Zbl0655.14001MR909240

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