Surfaces with pg = q = 2, K 2 = 6, and Albanese Map of Degree 2
Canadian journal of mathematics, Tome 65 (2013) no. 1, pp. 195-221

Voir la notice de l'article provenant de la source Cambridge University Press

We classify minimal surfaces of general type with ${{p}_{g}}=q=2$ and ${{K}^{2}}=6$ whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth irreducible components ${{\mathcal{M}}_{Ia}},\,{{\mathcal{M}}_{Ib}},\,{{\mathcal{M}}_{II}}$ of dimension 4, 4, 3, respectively.
DOI : 10.4153/CJM-2012-007-0
Mots-clés : 14J29, 14J10, surface of general type, abelian surface, Albanese map
Penegini, Matteo; Polizzi, Francesco. Surfaces with pg = q = 2, K 2 = 6, and Albanese Map of Degree 2. Canadian journal of mathematics, Tome 65 (2013) no. 1, pp. 195-221. doi: 10.4153/CJM-2012-007-0
@article{10_4153_CJM_2012_007_0,
     author = {Penegini, Matteo and Polizzi, Francesco},
     title = {Surfaces with pg = q = 2, {K} 2 = 6, and {Albanese} {Map} of {Degree} 2},
     journal = {Canadian journal of mathematics},
     pages = {195--221},
     year = {2013},
     volume = {65},
     number = {1},
     doi = {10.4153/CJM-2012-007-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-007-0/}
}
TY  - JOUR
AU  - Penegini, Matteo
AU  - Polizzi, Francesco
TI  - Surfaces with pg = q = 2, K 2 = 6, and Albanese Map of Degree 2
JO  - Canadian journal of mathematics
PY  - 2013
SP  - 195
EP  - 221
VL  - 65
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-007-0/
DO  - 10.4153/CJM-2012-007-0
ID  - 10_4153_CJM_2012_007_0
ER  - 
%0 Journal Article
%A Penegini, Matteo
%A Polizzi, Francesco
%T Surfaces with pg = q = 2, K 2 = 6, and Albanese Map of Degree 2
%J Canadian journal of mathematics
%D 2013
%P 195-221
%V 65
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-007-0/
%R 10.4153/CJM-2012-007-0
%F 10_4153_CJM_2012_007_0

[Ba87] [Ba87] Barth, W., Abelian surfaces with (1, 2)-polarization. In: Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987, pp. 41–84. Google Scholar

[BHPV03] [BHPV03] Barth, W., Hulek, K., Peters, C. A. M., and Van de Ven, A., Compact complex surfaces. Second ed. Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Folge. A Series of Modern Surveys in Mathematics, 4, Springer-Verlag, Berlin, 2004. Google Scholar

[BPS09] [BPS09] Bastianelli, F., Pirola, G. P., and Stoppino, L., Galois closure and Lagrangian varieties. Adv. Math. 225(2010), no. 6, 3463–3501. Google Scholar | DOI

[BL04] [BL04] Birkenhake, C. and Lange, H., Complex abelian varieties. Second ed., Grundlehren der MathematischenWissenschaften, 302, Springer-Verlag, Berlin, 2004. Google Scholar

[Ca90] [Ca90] Catanese, F., Footnotes to a theorem of I. Reider. In: Algebraic geometry (L'Aquila, 1988), Lecture Notes in Math., 1417, Springer, Berlin, 1990, pp. 67–74. Google Scholar

[Ca91] [Ca91] Catanese, F., Moduli and classification of irregular Kaehler manifolds (and algebraic varieties) with Albanese general type fibrations. Invent. Math. 104(1991), no. 2, 263–289. Google Scholar | DOI

[Ca11] [Ca11] Catanese, F., A superficial working guide to deformations and moduli, arxiv:1106.1368, to appear in the Handbook of Moduli, a volume in honour of David Mumford, to be published by International Press. Google Scholar

[F98] [F98] Friedman, R., Algebraic surfaces and holomorphic vector bundles. Universitext, Springer-Verlag, New York, 1998. Google Scholar

[GAP4] The GAP Group, GAP - Groups, algorhithms, and programming, Version 4.4.12, 2008 http://www.gap-system.org. Google Scholar

[HP02] [HP02] Hacon, C. D. and Pardini, R., Surfaces with p = q = 3. Trans. Amer. Math. Soc. 354(2002), no. 7, 2631–2638. Google Scholar | DOI

[Har79] [Har79] Harris, J., Galois groups of enumerative problems. Duke Math. J. 46(1979), no. 4, 685–724. Google Scholar | DOI

[HvM89] [HvM89] Horozov, E. and van Moerbeke, P., The full geometry of Kowalewski's top and (1, 2)-abelian surfaces. Comm. Pure Appl. Math. 42(1989), no. 4, 357–407. Google Scholar | DOI

[Man08] [Man08] M. Manetti, , Smoothing of singularities and deformation types of surfaces. In: Symplectic 4-manifolds and algebraic surfaces, Lecture Notes in Math., 1938, Springer, Berlin, 2008, pp. 169–230. Google Scholar

[Mu81] [Mu81] Mukai, S., Duality between D(X) and D() with its application to Picard sheaves. Nagoya Math. J. 81(1981), 153–175. Google Scholar

[Mu99] [Mu99] Mukai, S., Moduli of abelian surfaces and regular polyhedral groups. In Moduli of algebraic varieties and the monster, Proceedings, Sapporo, January 1999. Ed. I. Nakamura, Hokkaido Univ. 1999, pp. 68–74. Google Scholar

[Pe11] [Pe11] Penegini, M., The classification of isotrivially fibred surfaces with p= q = 2. with an appendix by S. Roellenske. Collect. Math. 62(2011), no. 3, 239–274. Google Scholar | DOI

[PP10] [PP10] Penegini, M. and Polizzi, F., On surfaces with p = q = 2, K = 5 and Albanese map of degree 3. arxiv:1011.4388. Google Scholar

[Pi02] [Pi02] Pirola, G. P., Surfaces with p = q = 3. Manuscripta Math. 108(2002), no. 2, 163–170. Google Scholar | DOI

[Rol10] [Rol10] Rollenske, S., Compact moduli for certain Kodaira fibrations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9(2010), no. 4, 851–874. Google Scholar

[Se06] [Se06] Sernesi, E., Deformations of algebraic schemes. Grundlehren der Mathematischen Wissenschaften, 334, Springer-Verlag, Berlin, 2006. Google Scholar

[Z03] [Z03] Zucconi, F., Surfaces with p = q = 2 and an irrational pencil. Canad. J. Math. 55(2003), no. 3, 649–672. Google Scholar | DOI

Cité par Sources :