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

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Abstract

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

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References

  1. Bombieri, E., Mumford, D.: Enriques’ classification of surfaces in char. p, III. Invent. math. 35(1), 197–232 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  2. Căldăraru, A.: Derived categories of twisted sheaves on Calabi-Yau manifolds. Ph.D. thesis, Cornell University (2000)

  3. Căldăraru, A.: Derived categories of sheaves: a skimming. Snowbird lectures in algebraic geometry. Contemp. Math. 388, 43–75 (2005)

    Article  Google Scholar 

  4. Căldăraru, A.: Fourier-Mukai transform for twisted sheaves. Ph.D. thesis, Universität Bonn (2010)

  5. Cossec, F., Dolgachev, I.: Enriques Surfaces I, vol. 76. Springer, Berlin (2012)

    MATH  Google Scholar 

  6. Honigs, K.: Derived equivalent surfaces and abelian varieties, and their zeta functions. Proc. Am. Math. Soc. 143(10), 4161–4166 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  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. Huybrechts, D.: Fourier-Mukai Transforms in Algebraic Geometry. Oxford University Press on Demand, Oxford (2006)

  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)

  10. Liedtke, C.: Arithmetic moduli and lifting of Enriques surfaces. J. Reine Angew. Math. 2015(706), 35–65 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Martınez, H.: Fourier-Mukai transform for twisted derived categories of surfaces. Rev. Colomb. Mat. 46(2), 205–228 (2012)

    MathSciNet  MATH  Google Scholar 

  12. Swan, R.G.: Hochschild cohomology of quasiprojective schemes. J. Pure Appl. Algebra 110(1), 57–80 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Bergen, Allégaten, 41 5007, Bergen, Norway

    Sofia Tirabassi

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  1. Sofia Tirabassi
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Correspondence to Sofia Tirabassi.

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Tirabassi, S. A note on the derived category of enriques surfaces in characteristic 2. Boll Unione Mat Ital 11, 121–124 (2018). https://doi.org/10.1007/s40574-016-0100-2

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  • DOI: https://doi.org/10.1007/s40574-016-0100-2

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