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Bollettino dell'Unione Matematica Italiana

, Volume 11, Issue 1, pp 121–124 | Cite as

A note on the derived category of enriques surfaces in characteristic 2

  • Sofia Tirabassi
Article
  • 71 Downloads

Abstract

We show that the (twisted) derived category “recognizes” the three different kinds of Enriques surfaces in characteristic 2.

Keywords

Derived category Algebraic surfaces Characteristic 2 

Mathematics Subject Classification

14J28 14J20 14F05 

Notes

Acknowledgments

I would like to thank Prof. C. Liedtke for asking me the question which this note answers at a conference in Berlin. I am also grateful to the unknown referee for many suggestions and improvements. It was him (or her) who encouraged me to pursue the variant of Theorem A proposed in the last section.

References

  1. 1.
    Bombieri, E., Mumford, D.: Enriques’ classification of surfaces in char. p, III. Invent. math. 35(1), 197–232 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Căldăraru, A.: Derived categories of twisted sheaves on Calabi-Yau manifolds. Ph.D. thesis, Cornell University (2000)Google Scholar
  3. 3.
    Căldăraru, A.: Derived categories of sheaves: a skimming. Snowbird lectures in algebraic geometry. Contemp. Math. 388, 43–75 (2005)CrossRefGoogle Scholar
  4. 4.
    Căldăraru, A.: Fourier-Mukai transform for twisted sheaves. Ph.D. thesis, Universität Bonn (2010)Google Scholar
  5. 5.
    Cossec, F., Dolgachev, I.: Enriques Surfaces I, vol. 76. Springer, Berlin (2012)zbMATHGoogle Scholar
  6. 6.
    Honigs, K.: Derived equivalent surfaces and abelian varieties, and their zeta functions. Proc. Am. Math. Soc. 143(10), 4161–4166 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Honigs, K., Lombardi, L., Tirabassi, S.: Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic. Preprint: arXiv:1606.02094 (2016)
  8. 8.
    Huybrechts, D.: Fourier-Mukai Transforms in Algebraic Geometry. Oxford University Press on Demand, Oxford (2006)Google Scholar
  9. 9.
    Liedtke, C.: Algebraic surfaces in positive characteristic. In: Birational Geometry, Rational Curves, and Arithmetic. Springer, New York Heidelberg Dordrecht London, pp. 229–292 (2013)Google Scholar
  10. 10.
    Liedtke, C.: Arithmetic moduli and lifting of Enriques surfaces. J. Reine Angew. Math. 2015(706), 35–65 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Martınez, H.: Fourier-Mukai transform for twisted derived categories of surfaces. Rev. Colomb. Mat. 46(2), 205–228 (2012)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Swan, R.G.: Hochschild cohomology of quasiprojective schemes. J. Pure Appl. Algebra 110(1), 57–80 (1996)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Unione Matematica Italiana 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway

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