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A few questions about curves on surfaces

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Abstract

In this note we address the following kind of question: let X be a smooth, irreducible, projective surface and \(D\) a divisor on X satisfying some sort of positivity hypothesis, then is there some multiple of D depending only on X which is effective or movable? We describe some examples, discuss some conjectures and prove some results that suggest that the answer should in general be negative, unless one puts some really strong hypotheses either on \(D\) or on \(X\).

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Authors and Affiliations

  1. Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Rome, Italy

    Ciro Ciliberto

  2. Department of Mathematics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Andreas Leopold Knutsen

  3. University of Illinois at Chicago, Math, Stat & CS, Room 411 SEO, 851 S Morgan St, M/C 249, Chicago, IL, 60607-7045, USA

    John Lesieutre

  4. Laboratoire de Mathmatiques “Nicolas Oresme”, Université de Caen Normandie, 14032, Caen Cedex, France

    Victor Lozovanu

  5. Department of mathematics, College of Natural Sciences, Colorado State University, 117 Statistics Building, Fort Collins, CO, 80523, USA

    Rick Miranda

  6. Department of Mathematics, Tufts University, 503 Boston Avenue, Bromfield-Pearson Room 106, Medford, MA, 02155, USA

    Yusuf Mustopa

  7. Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, UK

    Damiano Testa

Authors
  1. Ciro Ciliberto
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  2. Andreas Leopold Knutsen
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  3. John Lesieutre
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  4. Victor Lozovanu
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  5. Rick Miranda
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  6. Yusuf Mustopa
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  7. Damiano Testa
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Correspondence to Andreas Leopold Knutsen.

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Ciliberto, C., Knutsen, A.L., Lesieutre, J. et al. A few questions about curves on surfaces. Rend. Circ. Mat. Palermo, II. Ser 66, 195–204 (2017). https://doi.org/10.1007/s12215-016-0284-4

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  • DOI: https://doi.org/10.1007/s12215-016-0284-4

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