Classification of projective surfaces with small sectional genus : char p > 0

M. Andreatta; E. Ballico

Rendiconti del Seminario Matematico della Università di Padova (1990)

  • Volume: 84, page 175-193
  • ISSN: 0041-8994

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Andreatta, M., and Ballico, E.. "Classification of projective surfaces with small sectional genus : char $p$ &gt; $0$." Rendiconti del Seminario Matematico della Università di Padova 84 (1990): 175-193. <http://eudml.org/doc/108194>.

@article{Andreatta1990,
author = {Andreatta, M., Ballico, E.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {characteristic techniques; smooth projective surface; ample line bundle; adjunction mapping},
language = {eng},
pages = {175-193},
publisher = {Seminario Matematico of the University of Padua},
title = {Classification of projective surfaces with small sectional genus : char $p$ &gt; $0$},
url = {http://eudml.org/doc/108194},
volume = {84},
year = {1990},
}

TY - JOUR
AU - Andreatta, M.
AU - Ballico, E.
TI - Classification of projective surfaces with small sectional genus : char $p$ &gt; $0$
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1990
PB - Seminario Matematico of the University of Padua
VL - 84
SP - 175
EP - 193
LA - eng
KW - characteristic techniques; smooth projective surface; ample line bundle; adjunction mapping
UR - http://eudml.org/doc/108194
ER -

References

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  1. [A-B] M. Andreatta - E. Ballico, On the adjunction process over a surface in char. p, Manuscripta Math., 62 (1988), pp. 227-244. Zbl0698.14034MR963008
  2. [Bo] E. Bombieri, Methods of algebraic geometry in char. p and their applications, on «Algebraic Surfaces C.I.M.E. », Cortona (1977), pp. 57-96. 
  3. [Ca] F. Catanese, Pluricanonical Gorenstein curves, Enumerative Geometry and Classical Algebraic Geometry, Progr. in Math., Vol. 24, Birkhäuser (1982), pp. 51-95. Zbl0518.14017MR685764
  4. [De] M. Demazure, Surfaces de Del Pezzo, on « Seminaire sur les Singularitès des Surfaces », Lecture Notes in Mathematics, Vol. 777, Spinger-Verlag (1980), pp. 21-70. Zbl0444.14024MR579026
  5. [Ek] T. Ekedal, Canonical models of surfaces of general type in positive characteristic, I.H.E.S. Publ. Mathématiques (1988), pp. 97-144. Zbl0674.14028MR972344
  6. [Ja] J.P. Jouanolou, Théorèmes de Bertini et Applications, Progr. in Math., Vol. 42, Birkhäuser (1983). Zbl0519.14002MR725671
  7. [Ha] R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York (1977). Zbl0367.14001MR463157
  8. [Io] P. Ionescu, Embedded projective varieties of small invariants, Proc. of the Algebraic Geometry Conf., Bucharest (1982), pp. 142-186. Zbl0542.14024MR749942
  9. [La] A. Lanteri, Sulle superfici di grado 7, Istituto Lombardo (Rend. Sc.)mA115 (1987), pp. 171-189. 
  10. [Li1] L. Livorni, Classification of algebraic surfaces with sectional genus less than or equal to six. I: rational surfaces, Pac. Journal of Math., Vol. 113 (1984), pp. 93-114. Zbl0573.14013MR745598
  11. [Li2] L. Livorni, Classification of algebraic non ruled surfaces with sectional genus less than or equal to six, Nagoya Math. J., Vol. 100 (1985), pp. 1-9. Zbl0594.14028MR818155
  12. [Ok] C. Okonek, Über 2-codimensionale Untermannigfaltigkeiten vom Grad 7 im P4 und P5, Math. Z., 187 (1984), pp. 209-219. Zbl0575.14030MR753433
  13. [Ra] J. Rathmann, The uniform position principle for curves in char p, Math. Ann., 276 (1987), pp. 565-579. Zbl0595.14041MR879536
  14. [So1] A.J. Sommese, Hyperplane sections of projective surfaces. I: The adjunction mapping, Duke Math. J., 46 (1979), pp. 377-401. Zbl0415.14019MR534057
  15. [So2] A.J. Sommese, Ample divisors on Gorenstein varieties, Revue de l'Institute E. Cartan, Journées Complexe, Nancy, 10 (1986). Zbl0646.14007MR933787
  16. [S-VdV] A.J. Sommese - A. Van De Ven, On the Adjunction Mapping, Math. Ann., 278 (1987), pp. 593-603. Zbl0655.14001MR909240
  17. [VdV] A. Van De Ven, On the 2 connectedness of very ample divisors on a surface, Duke Math. J., 46 (1979), pp. 403-407. Zbl0458.14003MR534058
  18. [Da] O. Zariski, Algebraic surfaces, Springer-Verlag, Berlin-Heidelberg-New York (1971). Zbl0219.14020MR469915

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