DOI QR코드

DOI QR Code

Euler Characteristics of Log Calabi-Yau Threefolds

  • Lee, Nam-Hoon (Department of Mathematics Education, Hongik University)
  • Received : 2016.10.04
  • Accepted : 2017.06.01
  • Published : 2017.06.23

Abstract

For any even integer n, we show that there exists a log Calabi-Yau threefold (Y, D) such that the Euler characteristic of Y is n. Furthermore Y is smooth and D is smooth anticanonical section of Y that is a K3 surface.

Keywords

References

  1. P. W. Barth, K. Hulek, A. M. C. Peters, Van de Ven, Antonius Compact complex surfaces, Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 4. Springer-Verlag, Berlin, 2004.
  2. G. Bini, F. F. Favale, An Unbounded Family of log Calabi-Yau Pairs, arXiv:1608.08804
  3. G. Di. Cerbo, R. Svaldi, Log birational boundedness of Calabi-Yau pairs, arXiv:1608.02997
  4. M. Gross, A finiteness theorem for elliptic Calabi-Yau threefolds, Duke Math. J., 74(1994), no. 2, 271299. https://doi.org/10.1215/S0012-7094-94-07414-0
  5. C. Hacon, C. Xu, Boundedness of log Calabi-Yau pairs of Fano type, Math. Res. Lett., 22(2015), no. 6, 1699-1716. https://doi.org/10.4310/MRL.2015.v22.n6.a8
  6. B. Hunt, A bound on the Euler number for certain Calabi-Yau 3 -folds, J. Reine Angew. Math., 411(1990), 137170.
  7. J. Kollar, C. Xu, The dual complex of log Calabi-Yau pairs, arXiv:1503.08320 to appear in Invent. Math. (2016)