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The Fulton-MacPherson compactification is not a Mori dream space

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Abstract

We show that the Fulton-MacPherson compactification of the configuration space of n distinct labeled points in certain varieties of arbitrary dimension d, including projective space, is not a Mori dream space for n larger than \(d + 8\).

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Acknowledgements

The authors would like to thank W. Fulton for insightful conversations. P. Gallardo thanks the University of California, Riverside for its support. J. González was supported by a grant from the Simons Foundation (Award Number 710443). E. Routis was supported by the EPSRC grant ‘Classification, Computation, and Construction: New Methods in Geometry’ (EP/N03189X/1).

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Authors and Affiliations

  1. Department of Mathematics, University of California, 900 University Ave., Riverside, CA, 92521 Skye Hall, USA

    Patricio Gallardo & José Luis González

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

    Evangelos Routis

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  1. Patricio Gallardo
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  2. José Luis González
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  3. Evangelos Routis
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Correspondence to Patricio Gallardo.

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Gallardo, P., González, J.L. & Routis, E. The Fulton-MacPherson compactification is not a Mori dream space. Math. Z. 302, 2567–2583 (2022). https://doi.org/10.1007/s00209-022-03145-x

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