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ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC p

Year 2012, Volume: 5 Issue: 1, 128 - 139, 30.04.2012

Abstract


References

  • 1. Bonacini, P., Laudal’s Lemma in positive characteristic, J. Algebraic Geom. 18 (2009), no. 3, 459–475.
  • 2. Bonacini, P., On the plane section of an integral curve in positive characteristic, Proc. Am. Math. Soc., 136 (2008), no.7, 2289–2297.
  • 3. Ein, L., Stable vector bundles on projective spaces in char p > 0, Math. Ann., 254 (1980), no. 1, 53–72.
  • 4. Geramita, A.V., Maroscia, P. and Roberts, L. G., The Hilbert function of a reduced k-algebra, J. London Math. Soc., 28 2 (1983), 443–452.
  • 5. Gruson, L. and Peskine, C., Section plane d’une courbe gauche: postulation, Enumerative Geometry and Classical Algebraic Geometry (Nice, 1981), Progr. Math., no. 24, Birkh¨auser, Boston, Mass., 1982, pp. 33—35.
  • 6. Harris, J., The Genus of space curves, Math. Ann., 249 (1980), no. 3, 191-–204.
  • 7. Hartshorne, R., Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York, 1977.
  • 8. Kleiman, S. L., Geometry on Grassmannians and applications to splitting bundles and smooth- ing cycles, Inst. Hautes E´ tudes Sci. Publ. Math., No. 36 (1969), 281–297.
  • 9. Langer, A., Semistable sheaves in positive characteristic, Ann. of Math. (2) 159 (2004) no. 1, 251–276.
  • 10. Laudal, O. A., A generalized trisecant lemma, Algebraic Geometry (Proc. Sympos. Univ. Tromsø, Tromsø, 1977), Lecture Notes in Math., no. 687, Springer-Verlag, Berlin, 1978, pp. 112-–149.
  • 11. Maggioni, R. and Ragusa, A., The Hilbert function of generic plane sections of curves of P3, Inv. Math., 91 (1988), 253—258.
  • 12. Maggioni, R. and Ragusa, A., Construction of smooth curves of P3 with assigned Hilbert function and generators’ degrees, Le Matematiche, 42 (1987), no. 1-2, 195–209 (1989).
  • 13. Maruyama, M., Boundedness of semistable sheaves of small ranks, Nagoya Math. J., 78 (1980), 65–94.
  • 14. Mehta, V. B. and Ramanathan, A., Homogeneous bundles in characteristic p, in Algebraic geometry - open problems, Proc. Conf., Ravello/Italy 1982, Lect. Notes Math. 997, 315–320 (1983).
  • 15. Mezzetti, E. and Raspanti, I., A Laudal-type theorem for surfaces in P4, Commutative algebra and algebraic geometry, I (Italian) (Turin, 1990), Rend. Sem. Mat. Univ. Politec. Torino, 48 (1990), no. 4, 529–537 (1993).
  • 16. Mezzetti, E., The border cases of the lifting theorem for surfaces in P4, J. Reine Angew. Math., 433 (1992), 101–111.
  • 17. Mezzetti, E., Differential-geometric methods for the lifting problem and linear systems on plane curves, J. Algebraic Geom., 3 (1994), no. 3, 375–398.
  • 18. Milne, J. S., ’Etale cohomology, Princeton Mathematical Series, no. 33, Princeton University Press, Princeton, N.J., 1980.
  • 19. Okonek, C., Schneider, M., Spindler, H., Vector bundles on complex projective spaces, Progress in Mathematics, 3. Birkh¨auser, Boston, Mass., 1980.
  • 20. Roggero, M., Sulle sezioni di un fascio riflessivo di rango 2 definenti sottovariet`a integre, Boll. Un. Mat. Ital. D (6) 4 (1985), no. 1, 57–61 (1986).
  • 21. Roggero, M., Lifting problem for codimension two subvarieties in Pn+2: border cases, Geo- metric and combinatorial aspects of commutative algebra (Messina, 1999), 309–326, Lecture Notes in Pure and Appl. Math., 217, Dekker, New York, 2001.
  • 22. Roggero, M., Generalizations of “Laudal Trescano Lemma” to codimension 2 subvarieties in PN , Quaderni del Dipartimento di Matematica di Torino 23/2003.
  • 23. Shepherd-Barron, N. I., Semi-stability and reduction mod p, Topology, 37 (1998), 659–664.
  • 24. Strano, R., On the hyperplane sections of curves, Proceedings of the Geometry Conference (Milan and Gargnano, 1987), Rend. Sem. Mat. Fis. Milano, 57 (1987), 125–134 (1989).
  • 25. Tortora, A., On the lifting problem in codimension two, (English summary) Matematiche (Catania), 52 (1997), no. 1, 41–51 (1998).
Year 2012, Volume: 5 Issue: 1, 128 - 139, 30.04.2012

Abstract

References

  • 1. Bonacini, P., Laudal’s Lemma in positive characteristic, J. Algebraic Geom. 18 (2009), no. 3, 459–475.
  • 2. Bonacini, P., On the plane section of an integral curve in positive characteristic, Proc. Am. Math. Soc., 136 (2008), no.7, 2289–2297.
  • 3. Ein, L., Stable vector bundles on projective spaces in char p > 0, Math. Ann., 254 (1980), no. 1, 53–72.
  • 4. Geramita, A.V., Maroscia, P. and Roberts, L. G., The Hilbert function of a reduced k-algebra, J. London Math. Soc., 28 2 (1983), 443–452.
  • 5. Gruson, L. and Peskine, C., Section plane d’une courbe gauche: postulation, Enumerative Geometry and Classical Algebraic Geometry (Nice, 1981), Progr. Math., no. 24, Birkh¨auser, Boston, Mass., 1982, pp. 33—35.
  • 6. Harris, J., The Genus of space curves, Math. Ann., 249 (1980), no. 3, 191-–204.
  • 7. Hartshorne, R., Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York, 1977.
  • 8. Kleiman, S. L., Geometry on Grassmannians and applications to splitting bundles and smooth- ing cycles, Inst. Hautes E´ tudes Sci. Publ. Math., No. 36 (1969), 281–297.
  • 9. Langer, A., Semistable sheaves in positive characteristic, Ann. of Math. (2) 159 (2004) no. 1, 251–276.
  • 10. Laudal, O. A., A generalized trisecant lemma, Algebraic Geometry (Proc. Sympos. Univ. Tromsø, Tromsø, 1977), Lecture Notes in Math., no. 687, Springer-Verlag, Berlin, 1978, pp. 112-–149.
  • 11. Maggioni, R. and Ragusa, A., The Hilbert function of generic plane sections of curves of P3, Inv. Math., 91 (1988), 253—258.
  • 12. Maggioni, R. and Ragusa, A., Construction of smooth curves of P3 with assigned Hilbert function and generators’ degrees, Le Matematiche, 42 (1987), no. 1-2, 195–209 (1989).
  • 13. Maruyama, M., Boundedness of semistable sheaves of small ranks, Nagoya Math. J., 78 (1980), 65–94.
  • 14. Mehta, V. B. and Ramanathan, A., Homogeneous bundles in characteristic p, in Algebraic geometry - open problems, Proc. Conf., Ravello/Italy 1982, Lect. Notes Math. 997, 315–320 (1983).
  • 15. Mezzetti, E. and Raspanti, I., A Laudal-type theorem for surfaces in P4, Commutative algebra and algebraic geometry, I (Italian) (Turin, 1990), Rend. Sem. Mat. Univ. Politec. Torino, 48 (1990), no. 4, 529–537 (1993).
  • 16. Mezzetti, E., The border cases of the lifting theorem for surfaces in P4, J. Reine Angew. Math., 433 (1992), 101–111.
  • 17. Mezzetti, E., Differential-geometric methods for the lifting problem and linear systems on plane curves, J. Algebraic Geom., 3 (1994), no. 3, 375–398.
  • 18. Milne, J. S., ’Etale cohomology, Princeton Mathematical Series, no. 33, Princeton University Press, Princeton, N.J., 1980.
  • 19. Okonek, C., Schneider, M., Spindler, H., Vector bundles on complex projective spaces, Progress in Mathematics, 3. Birkh¨auser, Boston, Mass., 1980.
  • 20. Roggero, M., Sulle sezioni di un fascio riflessivo di rango 2 definenti sottovariet`a integre, Boll. Un. Mat. Ital. D (6) 4 (1985), no. 1, 57–61 (1986).
  • 21. Roggero, M., Lifting problem for codimension two subvarieties in Pn+2: border cases, Geo- metric and combinatorial aspects of commutative algebra (Messina, 1999), 309–326, Lecture Notes in Pure and Appl. Math., 217, Dekker, New York, 2001.
  • 22. Roggero, M., Generalizations of “Laudal Trescano Lemma” to codimension 2 subvarieties in PN , Quaderni del Dipartimento di Matematica di Torino 23/2003.
  • 23. Shepherd-Barron, N. I., Semi-stability and reduction mod p, Topology, 37 (1998), 659–664.
  • 24. Strano, R., On the hyperplane sections of curves, Proceedings of the Geometry Conference (Milan and Gargnano, 1987), Rend. Sem. Mat. Fis. Milano, 57 (1987), 125–134 (1989).
  • 25. Tortora, A., On the lifting problem in codimension two, (English summary) Matematiche (Catania), 52 (1997), no. 1, 41–51 (1998).
There are 25 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Paola Bonacını This is me

Publication Date April 30, 2012
Published in Issue Year 2012 Volume: 5 Issue: 1

Cite

APA Bonacını, P. (2012). ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC p. International Electronic Journal of Geometry, 5(1), 128-139.
AMA Bonacını P. ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC p. Int. Electron. J. Geom. April 2012;5(1):128-139.
Chicago Bonacını, Paola. “ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC P”. International Electronic Journal of Geometry 5, no. 1 (April 2012): 128-39.
EndNote Bonacını P (April 1, 2012) ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC p. International Electronic Journal of Geometry 5 1 128–139.
IEEE P. Bonacını, “ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC p”, Int. Electron. J. Geom., vol. 5, no. 1, pp. 128–139, 2012.
ISNAD Bonacını, Paola. “ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC P”. International Electronic Journal of Geometry 5/1 (April 2012), 128-139.
JAMA Bonacını P. ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC p. Int. Electron. J. Geom. 2012;5:128–139.
MLA Bonacını, Paola. “ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC P”. International Electronic Journal of Geometry, vol. 5, no. 1, 2012, pp. 128-39.
Vancouver Bonacını P. ON THE LIFTING PROBLEM IN P4 IN CHARACTERISTIC p. Int. Electron. J. Geom. 2012;5(1):128-39.