Publications and Preprints

  1. 24 rational curves on K3 surfaces (with S. Rams)
    submitted
    [Article in Mathematics ArXiv]

  2. K3 surfaces with 9 cusps in characteristic p (with T. Katsura)
    submitted
    [Article in Mathematics ArXiv]

  3. Hilbert modularity of some double octic Calabi--Yau threefolds (with S. Cynk, D. van Straten)
    submitted
    [Article in Mathematics ArXiv]

  4. Q_l-cohomology projective planes from Enriques surfaces in odd characteristic
    submitted
    [Article in Mathematics ArXiv]

  5. Moduli of Gorenstein Q-homology projective planes
    submitted
    [Article in Mathematics ArXiv]

  6. Zariski K3 surfaces (with T. Katsura)
    to appear in Revista Matemática Iberoamericana
    [Article in Mathematics ArXiv]

  7. Counting lines on surfaces, especially quintics (with S. Rams)
    to appear in Annali Scuola Normale Superiore
    [Article in Mathematics ArXiv]

  8. Q_l-cohomology projective planes and singular Enriques surfaces in characteristic two
    Épijournal de Géométrie Algébrique 3 (2019), 24pp.
    [Article in Mathematics ArXiv]

  9. Divisibilities among nodal curves
    Math. Res. Letters 25 (2018), 1359-1368.
    [Article in Mathematics ArXiv]

  10. At most 64 lines on smooth quartic surfaces (characteristic 2) (with S. Rams)
    Nagoya Math. J. 232 (2018), 76-95.
    [Article in Mathematics ArXiv]

  11. On Enriques surfaces with fours cusps (with S. Rams)
    Publ. RIMS 54 (2018), 433-468.
    [Article in Mathematics ArXiv]

  12. Dynamics on supersingular K3 surfaces
    Comment. Math. Helv. 91 (2016), 705-719.
    [Article in Mathematics ArXiv]

  13. Picard numbers of quintic surfaces
    Proc. LMS 110 (2015), 428-476. (free access link)
    [Article in Mathematics ArXiv]

  14. 112 lines on smooth quartic surfaces (characteristic 3) (with S. Rams)
    Quart. J. Math. 66 (2015), 941-951. (free access link)
    [Article in Mathematics ArXiv]

  15. Genus 1 fibrations on the supersingular K3 surface in characteristic 2 with Artin invariant 1 (with Noam D. Elkies)
    Asian J. Math. 19 (2015), 555-582.
    [Article in Mathematics ArXiv]

  16. 64 lines on smooth quartic surfaces (with S. Rams)
    Math. Ann. 362 (2015), 679-698. *
    [Article in Mathematics ArXiv]

  17. On quartics with lines of the second kind (with S. Rams)
    Adv. Geom. 14 (2014), 735-756.
    [Article in Mathematics ArXiv]

  18. The Barth quintic surface has Picard number 41 (with S. Rams)
    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XIII (2014), 533-549.
    [Article in Mathematics ArXiv]

  19. Abelian Fourfolds of Weil type and certain K3 Double Planes (with Giuseppe Lombardo, Chris Peters)
    Rend. Sem. Mat. Univ. Politec. Torino 71 (2013), 339-383
    [Article in Mathematics ArXiv]

  20. K3 surfaces with an automorphism of order 11
    Tohoku Math Journal 65 (2013), 515-522.
    [Article in Mathematics ArXiv]

  21. Two lectures on the arithmetic of K3 surfaces
    Arithmetic and Geometry of K3 surfaces and Calabi-Yau Threefolds, Fields Institute Communications 67 (2013), 71-99.
    [Article in Mathematics ArXiv]

  22. On the uniqueness of K3 surfaces with maximal singular fibre (with A. Schweizer)
    Annales de l'institut Fourier, 63 (2013) 689-713.
    [Article in Mathematics ArXiv]

  23. Modular forms and K3 surfaces (with Noam D. Elkies)
    Advances in Mathematics 240 (2013), 106-131.
    [Article in Mathematics ArXiv]

  24. Sandwich theorems for Shioda-Inose structures
    Izvestiya Mat. 77 (2013), 211-222.
    [Article in Mathematics ArXiv]

  25. Modularity of the Consani-Scholten quintic (with Luis Dieulefait and Ariel Pacetti)
    Documenta Math. 17 (2012), 953-987.
    [Article in Mathematics ArXiv]

  26. Two moduli spaces of abelian fourfolds with an automorphism of order five (with Bert van Geemen) *
    Int. J. Math. 23, No. 10 (2012).
    [Article in Mathematics ArXiv]

  27. Arithmetic of singular Enriques Surfaces (with K. Hulek)
    Algebra & Number Theory 6 (2012), no. 2, 195-230.
    [Article in Mathematics ArXiv]

  28. Enriques surfaces - Brauer groups and Kummer structures (with Alice Garbagnati)
    Michigan Math. J. 61 (2012), 297-330.
    [
    Article in Mathematics ArXiv]

  29. A note on the supersingular K3 surface of Artin invariant 1
    Journal of Pure and Applied Algebra 216 (2012), 1438-1441.
    [Article in Mathematics ArXiv]

  30. Non-liftable Calabi-Yau spaces (with S. Cynk)
    Arkiv för Matematik 50 (2012), 23-40.
    [Article in Mathematics ArXiv]

  31. Modularity of Maschke's octic and Calabi-Yau threefold
    Comm. Number Th. & Physics 5 (2011), 827-847.
    [Artikel im Mathematics ArXiv]

  32. Quintic surfaces with maximum and other Picard numbers
    Journal Math. Soc. Japan 63 (2011), 1187-1201.
    [Article in Mathematics ArXiv]

  33. Enriques Surfaces and jacobian elliptic K3 surfaces (with K. Hulek) *
    Math. Z. 268 (2011), 1025-1056.
    [Article in Mathematics ArXiv]

  34. Lifts of projective congruence subgroups (with I. Kiming, H. Verrill)
    J. London Math. Soc. (2011) 83 (1), 96-120.
    [Article in Mathematics ArXiv]

  35. Elliptic surfaces (with T. Shioda) *
    Algebraic geometry in East Asia - Seoul 2008, Advanced Studies in Pure Mathematics 60 (2010), 51-160.
    [Article in Mathematics ArXiv]

  36. The modularity of K3 surfaces with non-symplectic group actions (with R. Livne, N. Yui) *
    Math. Ann. 348 (2010), 333-355.
    [Article in Mathematics ArXiv]

  37. Lines on Fermat surfaces (with T. Shioda, R. van Luijk)
    Journal of Number Theory 130 (2010), 1939-1963.
    [Article in Mathematics ArXiv]

  38. K3 surfaces of Picard rank 20 over Q
    Algebra & Number Theory 4 (2010), no. 3, 335-356.
    [Article in Mathematics ArXiv]

  39. K3 surfaces with non-symplectic automorphism of 2-power order
    Journal of Algebra 323 (2010), 206-223.
    [Article in Mathematics ArXiv]

  40. CM newforms with rational coefficients
    Ramanujan Journal 19 (2009), 187-205.
    [Article in Mathematics ArXiv]

  41. Generalised Kummer constructions and Weil restrictions (with S. Cynk)
    Journal of Number Theory 129 (2009), 1965-1975.
    [Article in Mathematics ArXiv]

  42. Arithmetic of K3 surfaces
    Jahresbericht der DMV 111 (2009), 23-41.
    [Article in Mathematics ArXiv]

  43. Unirational Surfaces on the Noether Line (with C. Liedtke)
    Pacific J. Math. 239 (2009), 343-356.
    [Article in Mathematics ArXiv]

  44. Arithmetic of a singular K3 surface
    Michigan Math. J. 56 (2008), 513-527.
    [Article in Mathematics ArXiv]

  45. On Davenport-Stothers inequalities and elliptic surfaces in positive characteristic (with A. Schweizer)
    Quarterly J. Math. 59 (2008), 499-522.
    [Article in Mathematics ArXiv]

  46. Fields of definition of singular K3 surfaces
    Communications in Number Theory and Physics 1, 2 (2007), 307-321.
    [Article in Mathematics ArXiv]

  47. An interesting elliptic surface over an elliptic curve (with T. Shioda)
    Proc. Jap. Acad. 83, 3 (2007), 40-45.
    [Article in Mathematics ArXiv]

  48. Elliptic fibrations of some extremal K3 surfaces
    Rocky Mountain Journal of Mathematics 37, 2 (2007), 609-652.
    [Article in Mathematics ArXiv]

  49. The maximal singular fibres of elliptic K3 surfaces *
    Archiv der Mathematik 79, 4 (2006), 309-319.
    [Article in Mathematics ArXiv]

  50. Modularity of Calabi-Yau varieties (with K. Hulek, R. Kloosterman)
    In: Catanese et al. (eds.) - Global Aspects of Complex Geometry, Springer (2006).
    [Article in Mathematics ArXiv]

  51. Arithmetic of the [19,1,1,1,1,1] fibration (with J. Top) *
    Commentarii Mathematici Universitatis Sancti Pauli 55, 1 (2006), 9-16.
    [Article in Mathematics ArXiv]

  52. On the modularity of three Calabi-Yau threefolds with bad reduction at 11
    Canad. Math. Bull. 49 (2), 2006, 296-312.
    [Article in Mathematics ArXiv]

  53. New examples of modular rigid Calabi-Yau threefolds
    Collect. Math. 55, 2 (2004), 219-228.
    [Article in Mathematics ArXiv]

    Books (authored/edited)         

    1. Mordell-Weil lattices (with T. Shioda) [pdf]
      to appear in Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge

    2. Calabi-Yau Varieties: Arithmetic, Geometry and Physics (with R. Laza, N. Yui)
      Fields Institute Monographs, Vol. 34, x + 547 p., Springer (2015)

    3. Algebraic and Complex Geometry (with A. Frühbis-Krüger, R. Kloosterman)
      Springer PROMS 71, xii + 319 p., Springer (2014)

    4. Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds (with R. Laza, N. Yui)
      Fields Institute Communications, Vol. 67, xxvi + 602 p., Springer (2013)

      Notes and Supplements         

        Hecke eigenvalues of certain Hilbert modular forms [pdf]
        supplementing the paper 'Hilbert modularity of some double octic Calabi--Yau threefolds' with S. Cynk and D. van Straten

        Explicit matrices supplementing the paper 'Dynamics on supersingular K3 surfaces' [pdf]

        K3 families of high Picard rank [pdf]
        unpublished note, joint with N. D. Elkies

        Enriques surfaces and jacobian elliptic K3 surfaces [pdf]
        Oberwolfach Report OWR 2010-46 (Mini-Workshop Higher Dimensional Elliptic Fibrations)

        Table of eigenvalues of a Hilbert modular form [txt]
        supplementing the paper "Modularity of the Consani-Scholten quintic" with Luis Dieulefait and Ariel Pacetti

        MAGMA scripts supplementing the computations in section 6 and section 7 of paper "Lines on Fermat surfaces" with T. Shioda and R. van Luijk

        A modular Calabi-Yau threefold with CM by \Q(\sqrt{-23}) (with S. Cynk)   [pdf]
        Supplement to the paper "Generalised Kummer constructions and Weil restrictions" with S. Cynk

      Addenda & Corrigenda         

        [RS] Proposition 7.1 in the published version needs an extra assumption, as pointed out by Tomasz Szemberg and Davide Veniani: if any three coplanar lines meet in a single point, then the residual line also contains this point (see the latest arXiv version)

        [vGS] In 1.8, \theta[10//10]^4 should be \theta[01//10]^4 [brought up by Kenji Koike]

        [HS1] In 3.4, just below (5), the rational elliptic surface arising as a quotient will have zero or one multiple fibre (and possibly no section) [pointed out by Hisanori Ohashi]

        [SSh2] In Theorem 5.1, the elliptic surface ought to be sufficiently general in order to be determined by its discriminant (cf. Heckmann, Looijenga: The moduli space of rational elliptic surfaces, Advanced Studies in Pure Math. 36, Algebraic Geometry (Azumino 2000), 185-248) [pointed out by Nick Katz]

        [LSY] The proof of Lemma 4 tacitly uses that we have h^{2,0}=1 for a K3 surface.

        [Archiv] In 6.2, the case v_0(Delta) = 21 corresponds exactly to c = sqrt(e).

        [ST] One summand of B in Section 2 ought to be 15t^4.

      Dissertation         

        Hecke eigenforms and the arithmetic of singular K3 surfaces
        [Abstract, thesis]