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Cyclic coverings and higher order embeddings of algebraic varieties
Author(s):
Thomas
Bauer;
Sandra
Di Rocco;
Tomasz
Szemberg
Journal:
Trans. Amer. Math. Soc.
353
(2001),
877-891.
MSC (2000):
Primary 14C20
Posted:
November 14, 2000
MathSciNet review:
1707697
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Abstract:
In the present paper we study higher order embeddings in the context of cyclic coverings. Analyzing the positivity of the line bundle downstairs and its relationship with the branch divisor, we provide criteria for its pull-back to define an embedding of given order. We show that the obtained criteria are sharp. Finally, we apply them to various - sometimes seemingly unrelated-problems in algebraic geometry.
References:
- 1.
- Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. Ergeb. Math. Grenzgeb. (3) 4, Springer-Verlag, 1984. MR 86c:32026
- 2.
- Bauer, Th., Szemberg, T.: Higher order embeddings of abelian varieties. Math. Z. 224, 449-455 (1997) MR 98a:14009
- 3.
- Bauer, Th., Szemberg, T.: Primitive higher order embeddings of abelian surfaces. Trans. Amer. Math. Soc. 349, 1675-1683 (1997) MR 97h:14005
- 4.
- Beltrametti, M.C., Di Rocco, S., Sommese, A.J.: On higher order embeddings of Fano threefolds by the anticanonical linear system. J. Math. Sci. Univ. Tokyo, 5, 75-97 (1998). MR 99d:14036
- 5.
- Bauer, Th., Di Rocco S., Szemberg, T.: Generation of jets on K3 surfaces. J. Pure Appl. Algebra, 146, 17-27 (2000). CMP 2000:07
- 6.
- Beltrametti M.C., Francia P., Sommese A.J.: On Reider's method and higher order embeddings. Duke Math. J. 58, 425-439 (1989) MR 90h:14021
- 7.
- Beltrametti, M.C., Sommese, A.J.: The Adjunction Theory of Complex Projective Varieties. Expositions in Mathematics, 16, Walter de Gruyter, Berlin (1995). MR 96f:14004
- 8.
- Beltrametti, M.C., Sommese, A.J.: On the preservation of
 -very ampleness under adjunction. Math. Z. 212, 257-283 (1993) MR 94a:14002 - 9.
- Beltrametti, M.C., Sommese, A.J.: On
 -jet ampleness. Complex analysis and geometry (Ancona, Vincenzo, eds.), New York, Plenum Press, 1993, pp. 355-376. MR 94g:14006 - 10.
- Beltrametti, M.C., Sommese, A.J.: Notes on embeddings of blowups, J. Algebra 186, 861-871 (1996) MR 97m:14004
- 11.
- Beltrametti, M.C., Szemberg, T.: On higher order embeddings of Calabi-Yau threefolds, preprint
- 12.
- Ciliberto, C., Miranda, R.: Degenerations of planar linear systems, J. Reine Angew. Math. 501, 191-200 (1998) CMP 98:16
- 13.
- Debarre, O., Hulek, K., Spandaw, J.: Very ample linear systems on abelian varieties. Math. Ann. 300, 181-202 (1994) MR 95k:14065
- 14.
- Demailly, J.-P.: Singular Hermitian metrics on positive line bundles. Complex algebraic varieties (Bayreuth, 1990), Lect. Notes Math. 1507, Springer-Verlag, 1992, pp. 87-104. MR 93g:32044
- 15.
- Demailly, J.-P.:
 vanishing theorems for positive line bundles and adjunction theory. In: Transcendental methods in algebraic geometry (Cetraro, 1994), Lect. Notes Math. 1646, Springer-Verlag, 1996, pp. 1-97. MR 99k:32051 - 16.
- Di Rocco S.:
 -very ample line bundles on Del Pezzo surfaces. Math. Nachr. 179, 47-56 (1996) MR 97h:14007 - 17.
- Di Rocco S.: Generation of
 -jets on toric varieties. Math Z. 231, 169-188 (1999) CMP 99:14 - 18.
- Geramita, A. V., Gimigliano G., and Harbourne B.: Projectively normal but superabundant embeddings of rational surfaces in projective space. J. of Algebra 169, 791-804, (1994). MR 96f:14044
- 19.
- Gimigliano, A.: Our thin knowledge of fat points. The Curves Seminar at Queen's, Vol. VI (Kingston, ON, 1989), Exp. No. B, 50 pp., Queen's Papers in Pure and Appl. Math., 83, Queen's Univ., Kingston, ON, 1989. MR 91a:14007
- 20.
- Lazarsfeld, R.: Lectures on linear series. Park City/IAS Mathematics series vol. 3, 161-219 (1993) MR 98h:14008
- 21.
- Mignon, T.: Systèmes de courbes planes à singularités: le cas des multiplicités inférieures ou égales à quatre. Preprint
- 22.
- Xu, G: Ample line bundles on smooth surfaces. J. Reine. Angew. Math. 469, 199-209 (1995) MR 96k:14003
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Additional Information:
Thomas
Bauer
Affiliation:
Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstraße $1\frac12$, D-91054 Erlangen, Germany
Address at time of publication:
Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße, D-35032 Marburg, Germany
Email:
tbauer@mathematik.uni-marburg.de
Sandra
Di Rocco
Affiliation:
KTH, Department of Mathematics, S-100 44 Stockholm, Sweden
Address at time of publication:
Department of Mathematics, Yale University, PO Box 208229, Hillhouse Ave. 70, New Haven, Connecticut 05620-8229
Email:
sandra.dirocco@math.yale.edu
Tomasz
Szemberg
Affiliation:
Instytut Matematyki, Uniwersytet Jagiellonski, Reymonta 4, PL-30-059 Kraków, Poland
Address at time of publication:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email:
szemberg@math.lsa.umich.edu
DOI:
10.1090/S0002-9947-00-02606-4
PII:
S 0002-9947(00)02606-4
Received by editor(s):
February 28, 1999
Received by editor(s) in revised form:
June 3, 1999
Posted:
November 14, 2000
Additional Notes:
The third author was supported by a research grant of Polish Academy of Sciences and KBN grant 2 P03A 008 16
Copyright of article:
Copyright
2000,
American Mathematical Society
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