On the topological index of irregular surfaces
Authors:
M. A. Barja, J. C. Naranjo and G. P. Pirola
Journal:
J. Algebraic Geom. 16 (2007), 435-458
DOI:
https://doi.org/10.1090/S1056-3911-06-00454-1
Published electronically:
December 26, 2006
MathSciNet review:
2306275
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Abstract |
References |
Additional Information
Abstract: We study the topological index of some irregular surfaces that we call generalized Lagrangian. We show that under certain hypotheses on the base locus of the Lagrangian system the topological index is non-negative. For the minimal surfaces of general type with $q=4$ and $p_g=5$ we prove the same statement without any hypothesis.
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Laz Lazarsfeld, R., Positivity in Algebraic Geometry, II. Ergebnisse Der Mathematik (3), Springer-Verlag, Berlin, 2005.
Am:wb Amorós, J.; Burger, M.; Corlette, K.; Kotschick, D.; Toledo, D., Fundamental Groups of Compact Kähler Manifolds. Mathematical Surveys and Monographs, 44, 1996.
BPV Barth, W.; Peters, C.; Van de Ven, A., Compact Complex Surfaces. Ergebnisse der Mathematik (3), Springer-Verlag, Berlin, 1984.
Cat Catanese, F., Fibred surfaces, varieties isogenous to a product and related moduli spaces. American J. of Math. 122 (2000), 1–44.
Cat2 Catanese, F., Moduli and classification of irregular Kaehler manifolds (and algebraic varieties) with Albanese general type fibrations, Invent. Math. 104 (1991), 263–289.
Cam Campana, F., Remarques sur les groupes de Kähler nilpotents. Ann. Sci. ENS 28 (1995), 307–316.
Miy Miyaoka, Y., The maximal number of quotient singularities on surfaces with given numerical invariants. Math. Ann. 268 (1984), 159–171.
Morgan Morgan, J., The Algebraic Topology of smooth algebraic varieties. Publ. IHES 48 (1978), 137–204.
Se Serrano, F., Isotrivial fibred surfaces. Ann. Mat. Pura Appl. 171 (1996), 63–81.
SVdV Sommese, A.J.; Van de Ven, A., Homotopy groups of pullbacks of varieties. Nagoya Math. J. 102 (1986), 79–90.
Xiao Xiao, G., Irregular families of hyperelliptic curves. Algebraic Geometry and Algebraic Number Theory (Tianjin) (1989–1990), 152–156.
Xiao2 Xiao, G., L’irrégularité des surfaces de type général dont le système canonique est composé d’un pinceau. Compositio Math. 56 (1985), 251–257.
Reider Reider, I., Vector bundles of rank $2$ and linear systems on algebraic surfaces. Annals of Mathematics 127 (1988), 309–316.
Pi:Du Pirola, G.P., Curves on generic Kummer varieties. Duke Math. J. 59 (1989), 701–708.
Pi:Xiao Pirola, G.P., On a conjecture of Xiao. J. Reine Angew. Math. 431 (1992), 75–89.
Bog:Tsc Bogomolov, F.; Tschinkel, Y., Lagrangian subvarieties of Abelian fourfolds. Asian J. Math. 4 (2000), 19–36.
Laz Lazarsfeld, R., Positivity in Algebraic Geometry, II. Ergebnisse Der Mathematik (3), Springer-Verlag, Berlin, 2005.
Additional Information
M. A. Barja
Affiliation:
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, ETSEIB Avda. Diagonal 647, 08028 Barcelona, Spain
Email:
Miguel.Angel.Barja@upc.edu
J. C. Naranjo
Affiliation:
Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain
MR Author ID:
318430
ORCID:
0000-0003-1989-4924
Email:
jcnaranjo@ub.edu
G. P. Pirola
Affiliation:
Dipartimento di Matematica, Università di Pavia, Via Ferrata, 1, 27100 Pavia, Italy
MR Author ID:
139965
Email:
pirola@dimat.unipv.it
Received by editor(s):
June 1, 2005
Received by editor(s) in revised form:
March 20, 2006
Published electronically:
December 26, 2006
Additional Notes:
The first author was partially supported by the Proyecto de Investigación BFM2003-06001 and ACI-2003. The second author was partially supported by the Proyecto de Investigación BFM2003-02914 and ACI-2003. The third author was partially supported by (1) PRIN 2003 “Spazi di moduli e teoria di Lie"; (2) Gnsaga; (3) Far 2004 (PV): Varietà algebriche, calcolo algebrico, grafi orientati e topologici
