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Nef cones of Hilbert schemes of points on surfaces

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Barbara Bolognese
  • Jack Huizenga
  • Yinbang Lin
  • Eric Riedl
  • Benjamin Schmidt

External Research Organisations

  • Northeastern University
  • Pennsylvania State University
  • University of Illinois at Chicago
  • The Ohio State University
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  • Citations
    • Citation Indexes: 14
  • Captures
    • Readers: 5
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Details

Original languageEnglish
Pages (from-to)907-930
Number of pages24
JournalAlgebra and Number Theory
Volume10
Issue number4
Publication statusPublished - 2016
Externally publishedYes

Abstract

Let X be a smooth projective surface of irregularity 0. The Hilbert scheme X[n] of n points on X parametrizes zero-dimensional subschemes of X of length n. We discuss general methods for studying the cone of ample divisors on X[n]. We then use these techniques to compute the cone of ample divisors on X[n] for several surfaces where the cone was previously unknown. Our examples include families of surfaces of general type and del Pezzo surfaces of degree 1. The methods rely on Bridgeland stability and the positivity lemma of Bayer and Macrì.

Cite this

Nef cones of Hilbert schemes of points on surfaces. / Bolognese, Barbara; Huizenga, Jack; Lin, Yinbang et al.
In: Algebra and Number Theory, Vol. 10, No. 4, 2016, p. 907-930.

Research output: Contribution to journal › Article › Research › peer review

Bolognese, B, Huizenga, J, Lin, Y, Riedl, E, Schmidt, B, Woolf, M & Zhao, X 2016, 'Nef cones of Hilbert schemes of points on surfaces', Algebra and Number Theory, vol. 10, no. 4, pp. 907-930. https://doi.org/10.2140/ant.2016.10.907
Bolognese, B., Huizenga, J., Lin, Y., Riedl, E., Schmidt, B., Woolf, M., & Zhao, X. (2016). Nef cones of Hilbert schemes of points on surfaces. Algebra and Number Theory, 10(4), 907-930. https://doi.org/10.2140/ant.2016.10.907
Bolognese B, Huizenga J, Lin Y, Riedl E, Schmidt B, Woolf M et al. Nef cones of Hilbert schemes of points on surfaces. Algebra and Number Theory. 2016;10(4):907-930. doi: 10.2140/ant.2016.10.907
Bolognese, Barbara ; Huizenga, Jack ; Lin, Yinbang et al. / Nef cones of Hilbert schemes of points on surfaces. In: Algebra and Number Theory. 2016 ; Vol. 10, No. 4. pp. 907-930.
Download
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title = "Nef cones of Hilbert schemes of points on surfaces",
abstract = "Let X be a smooth projective surface of irregularity 0. The Hilbert scheme X[n] of n points on X parametrizes zero-dimensional subschemes of X of length n. We discuss general methods for studying the cone of ample divisors on X[n]. We then use these techniques to compute the cone of ample divisors on X[n] for several surfaces where the cone was previously unknown. Our examples include families of surfaces of general type and del Pezzo surfaces of degree 1. The methods rely on Bridgeland stability and the positivity lemma of Bayer and Macr{\`i}.",
author = "Barbara Bolognese and Jack Huizenga and Yinbang Lin and Eric Riedl and Benjamin Schmidt and Matthew Woolf and Xiaolei Zhao",
note = "Funding information: J. Huizenga was partially supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship. B. Schmidt was partially supported by NSF grant DMS-1523496 (PI Emanuele Macr{\`i}) and a Presidential Fellowship of the Ohio State University.",
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TY - JOUR

T1 - Nef cones of Hilbert schemes of points on surfaces

AU - Bolognese, Barbara

AU - Huizenga, Jack

AU - Lin, Yinbang

AU - Riedl, Eric

AU - Schmidt, Benjamin

AU - Woolf, Matthew

AU - Zhao, Xiaolei

N1 - Funding information: J. Huizenga was partially supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship. B. Schmidt was partially supported by NSF grant DMS-1523496 (PI Emanuele Macrì) and a Presidential Fellowship of the Ohio State University.

PY - 2016

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N2 - Let X be a smooth projective surface of irregularity 0. The Hilbert scheme X[n] of n points on X parametrizes zero-dimensional subschemes of X of length n. We discuss general methods for studying the cone of ample divisors on X[n]. We then use these techniques to compute the cone of ample divisors on X[n] for several surfaces where the cone was previously unknown. Our examples include families of surfaces of general type and del Pezzo surfaces of degree 1. The methods rely on Bridgeland stability and the positivity lemma of Bayer and Macrì.

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