Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

Online
ISSN
1615-7168
See all formats and pricing
More options …
Volume 17, Issue 1

Issues

A note on surfaces with pg = q = 2 and an irrational fibration

Matteo Penegini / Francesco Polizzi
  • Corresponding author
  • Dipartimento di Matematica e Informatica, Università della Calabria, Cubo 30B, 87036 Arcavacata di Rende (Cosenza), Italy
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-02-17 | DOI: https://doi.org/10.1515/advgeom-2016-0031

Abstract

We study several examples of surfaces with pg = q = 2 and maximal Albanese dimension that are endowed with an irrational fibration.

Keywords: Surfaces of general type; fibrations; Albanese map.

MSC 2010: 14J29

Communicated by: A. Sommese

References

  • [1]

    M. Atiyah, On the Krull-Schmidt theorem with application to sheaves. Bull. Soc. Math. France 84 (1956), 307–317. MR0086358 Zbl 0072.18101Google Scholar

  • [2]

    M. F. Atiyah, Vector bundles over an elliptic curve. Proc. London Math. Soc. (3) 7 (1957), 414–452. MR0131423 Zbl 0084.17305Google Scholar

  • [3]

    M. A. Barja, Lower bounds of the slope of fibred threefolds. Internat. J. Math. 11 (2000), 461–491. MR1768169 Zbl 1100.14519Google Scholar

  • [4]

    W. Barth, Abelian surfaces with (1,2)-polarization. In: Algebraic geometry, Sendai, 1985, volume 10 of Adv. Stud. Pure Math., 41–84, North-Holland 1987. MR946234 Zbl 0639.14023Google Scholar

  • [5]

    W. P. Barth, K. Hulek, C. A. M. Peters, A. Van de Ven, Compact complex surfaces. Springer 2004. Zbl 1036.14016Google Scholar

  • [6]

    I. C. Bauer, F. Catanese, R. Pignatelli, Complex surfaces of general type: some recent progress. In: Global aspects of complex geometry, 1–58, Springer 2006. MR2264106 Zbl 1118.14041Google Scholar

  • [7]

    A. Beauville, Annulation du H1 et systèmes paracanoniques sur les surfaces. J. Reine Angew. Math. 388 (1988), 149–157. MR944188 Zbl 0639.14017Google Scholar

  • [8]

    C. Birkenhake, H. Lange, Complex abelian varieties. Springer 2004. MR2062673 Zbl 1056.14063Google Scholar

  • [9]

    F. Catanese, Fibred surfaces, varieties isogenous to a product and related moduli spaces. Amer. J. Math. 122 (2000), 1–44. MR1737256 Zbl 0983.14013Google Scholar

  • [10]

    F. Catanese, C. Ciliberto, M. Mendes Lopes, On the classification of irregular surfaces of general type with nonbirational bicanonical map. Trans. Amer. Math. Soc. 350 (1998), 275–308. MR1422597 Zbl 0889.14019Google Scholar

  • [11]

    F. Catanese, M. Dettweiler, Answer to a question by Fujita on variation of Hodge structure. arXiv:1311.3232v1 [math.AG]Google Scholar

  • [12]

    J. A. Chen, C. D. Hacon, A surface of general type with pg = q = 2 and KX2 = 5. Pacific J. Math. 223 (2006), 219–228. MR2221025 Zbl 1112.14047Google Scholar

  • [13]

    O. Debarre, Inégalités numériques pour les surfaces de type général. Bull. Soc. Math. France 110 (1982), 319–346. MR688038 Zbl 0543.14026Google Scholar

  • [14]

    E. Freitag, Über die Struktur der Funktionenkörper zu hyperabelschen Gruppen. I. J. Reine Angew. Math. 247 (1971), 97–117. MR0281689 Zbl 0232.10018Google Scholar

  • [15]

    R. Friedman, Algebraic surfaces and holomorphic vector bundles. Springer 1998. MR1600388 Zbl 0902.14029Google Scholar

  • [16]

    T. Fujita, On Kähler fiber spaces over curves. J. Math. Soc. Japan 30 (1978), 779–794. MR513085 Zbl 0393.14006Google Scholar

  • [17]

    T. Fujita, The sheaf of relative canonical forms of a Kähler fiber space over a curve. Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), 183–184. MR510945 Zbl 0412.32029Google Scholar

  • [18]

    C. D. Hacon, R. Pardini, Surfaces with pg = q = 3. Trans. Amer. Math. Soc. 354 (2002), 2631–2638. MR1895196 Zbl 1009.14004Google Scholar

  • [19]

    R. Hartshorne, Ample vector bundles on curves. Nagoya Math. J. 43 (1971), 73–89. MR0292847 Zbl 0218.14018 Zbl 0205.25402Google Scholar

  • [20]

    R. Hartshorne, Algebraic geometry. Springer 1977. MR0463157 Zbl 0367.14001Google Scholar

  • [21]

    G. R. Kempf, Complex abelian varieties and theta functions. Springer 1991. MR1109495 Zbl 0752.14040Google Scholar

  • [22]

    J. Kollár, Higher direct images of dualizing sheaves. I. Ann. of Math. (2) 123 (1986), 11–42. MR825838 Zbl 0598.14015Google Scholar

  • [23]

    M. M. Lopes, R. Pardini, The geography of irregular surfaces. In: Current developments in algebraic geometry, volume 59 of Math. Sci. Res. Inst. Publ., 349–378, Cambridge Univ. Press 2012. MR2931875 Zbl 1255.14028Google Scholar

  • [24]

    M. Mendes Lopes, R. Pardini, G. P. Pirola, Continuous families of divisors, paracanonical systems and a new inequality for varieties of maximal Albanese dimension. Geom. Topol. 17 (2013), 1205–1223. MR3070524 Zbl 1316.14016Google Scholar

  • [25]

    R. Pardini, Abelian covers of algebraic varieties. J. Reine Angew. Math. 417 (1991), 191–213. MR1103912 Zbl 0721.14009Google Scholar

  • [26]

    M. Penegini, The classification of isotrivially fibred surfaces with pg = q = 2. Collect. Math. 62 (2011), 239–274. MR2825713 Zbl 1228.14035Google Scholar

  • [27]

    M. Penegini, On the classification of surfaces of general type with pg = q = 2. Boll. Unione Mat. Ital. (9) 6 (2013), 549–563. MR3202839Google Scholar

  • [28]

    M. Penegini, F. Polizzi, On surfaces with pg = q = 2, K2 = 5 and Albanese map of degree 3. Osaka J. Math. 50 (2013), 643–686. MR3128997 Zbl 1288.14026Google Scholar

  • [29]

    M. Penegini, F. Polizzi, Surfaces with pg = q = 2, K2 = 6, and Albanese map of degree 2. Canad. J. Math. 65 (2013), 195–221. MR3004463 Zbl 1258.14045Google Scholar

  • [30]

    M. Penegini, F. Polizzi, A new family of surfaces with pg = q = 2 and K2 = 6 whose Albanese map has degree 4. J. Lond. Math. Soc. (2) 90 (2014), 741–762. MR3291798 Zbl 1325.14056Google Scholar

  • [31]

    G. P. Pirola, Surfaces with pg = q = 3. Manuscripta Math. 108 (2002), 163–170. MR1918584 Zbl 0997.14009Google Scholar

  • [32]

    F. Polizzi, Numerical properties of isotrivial fibrations. Geom. Dedicata 147 (2010), 323–355. MR2660583 Zbl 1202.14037Google Scholar

  • [33]

    F. Serrano, Isotrivial fibred surfaces. Ann. Mat. Pura Appl. (4) 171 (1996), 63–81. MR1441865 Zbl 0884.14016Google Scholar

  • [34]

    C. Simpson, Subspaces of moduli spaces of rank one local systems. Ann. Sci. École Norm. Sup. (4) 26 (1993), 361–401. MR1222278 Zbl 0798.14005Google Scholar

  • [35]

    G. Xiao, Surfaces fibrées en courbes de genre deux. Springer 1985. MR872271 Zbl 0579.14028Google Scholar

  • [36]

    G. Xiao, Fibered algebraic surfaces with low slope. Math. Ann. 276 (1987), 449–466. MR875340 Zbl 0596.14028Google Scholar

  • [37]

    F. Zucconi, Generalized hyperelliptic surfaces. Trans. Amer. Math. Soc. 355 (2003), 4045–4059. MR1990574 Zbl 1052.14044Google Scholar

  • [38]

    F. Zucconi, Surfaces with pg = q = 2 and an irrational pencil. Canad. J. Math. 55 (2003), 649–672. MR1980618 Zbl 1053.14042Google Scholar

About the article

Received: 2014-12-09

Revised: 2015-03-16

Published Online: 2017-02-17

Published in Print: 2017-01-01


Citation Information: Advances in Geometry, Volume 17, Issue 1, Pages 61–73, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2016-0031.

Export Citation

© 2017 by Walter de Gruyter Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in