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Symmetric products of a semistable degeneration of surfaces

Article

Abstract

We explicitly construct a V-normal crossing Gorenstein canonical model of the relative symmetric products of a local semistable degeneration of surfaces without a triple point by means of toric geometry. Using this model, we calculate the stringy E-polynomial of the relative symmetric product. We also construct a minimal model of degeneration of Hilbert schemes explicitly.

Notes

Acknowledgements

The author would like to thank M. Brion, M. Lehn, and T. Yasuda for their interest and helpful comments. He also thanks the anonymous referee for giving him valuable comments. This work is partially supported by JSPS Grants-in-aid for young scientists (B) 26800025.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and EngineeringWaseda UniversityTokyoJapan

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