*24 rational curves on K3 surfaces (with S. Rams)*

submitted

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

submitted

[Article in Mathematics ArXiv]**Q**_l-cohomology projective planes from Enriques surfaces in odd characteristic

submitted

[Article in Mathematics ArXiv]*Moduli of Gorenstein***Q**-homology projective planes

submitted

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

to appear in Journal of Number Theory

[Article in Mathematics ArXiv]*Zariski K3 surfaces (with T. Katsura)*

to appear in Revista Matemática Iberoamericana

[Article in Mathematics ArXiv]*Counting lines on surfaces, especially quintics (with S. Rams)*

to appear in Annali Scuola Normale Superiore

[Article in Mathematics ArXiv]**Q**_l-cohomology projective planes and singular Enriques surfaces in characteristic two

Épijournal de Géométrie Algébrique**3**(2019), 24pp.

[Article in Mathematics ArXiv]*Divisibilities among nodal curves*

Math. Res. Letters**25**(2018), 1359-1368.

[Article in Mathematics ArXiv]*At most 64 lines on smooth quartic surfaces (characteristic 2) (with S. Rams)*

Nagoya Math. J.**232**(2018), 76-95.

[Article in Mathematics ArXiv]*On Enriques surfaces with fours cusps (with S. Rams)*

Publ. RIMS**54**(2018), 433-468.

[Article in Mathematics ArXiv]*Dynamics on supersingular K3 surfaces*

Comment. Math. Helv.**91**(2016), 705-719.

[Article in Mathematics ArXiv]*Picard numbers of quintic surfaces*

Proc. LMS**110**(2015), 428-476. (free access link)

[Article in Mathematics ArXiv]*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]*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]*64 lines on smooth quartic surfaces (with S. Rams)*

Math. Ann.**362**(2015), 679-698. *

[Article in Mathematics ArXiv]*On quartics with lines of the second kind (with S. Rams)*

Adv. Geom.**14**(2014), 735-756.

[Article in Mathematics ArXiv]*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]*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]*K3 surfaces with an automorphism of order 11*

Tohoku Math Journal**65**(2013), 515-522.

[Article in Mathematics ArXiv]*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]*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]*Modular forms and K3 surfaces (with Noam D. Elkies)*

Advances in Mathematics**240**(2013), 106-131.

[Article in Mathematics ArXiv]*Sandwich theorems for Shioda-Inose structures*

Izvestiya Mat.**77**(2013), 211-222.

[Article in Mathematics ArXiv]*Modularity of the Consani-Scholten quintic (with Luis Dieulefait and Ariel Pacetti)*

Documenta Math.**17**(2012), 953-987.

[Article in Mathematics ArXiv]*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]*Arithmetic of singular Enriques Surfaces (with K. Hulek)*

Algebra & Number Theory**6**(2012), no. 2, 195-230.

[Article in Mathematics ArXiv]*Enriques surfaces - Brauer groups and Kummer structures (with Alice Garbagnati)*

Michigan Math. J.**61**(2012), 297-330.

[Article in Mathematics ArXiv]*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]*Non-liftable Calabi-Yau spaces (with S. Cynk)*

Arkiv för Matematik**50**(2012), 23-40.

[Article in Mathematics ArXiv]*Modularity of Maschke's octic and Calabi-Yau threefold*

Comm. Number Th. & Physics**5**(2011), 827-847.

[Artikel im Mathematics ArXiv]*Quintic surfaces with maximum and other Picard numbers*

Journal Math. Soc. Japan**63**(2011), 1187-1201.

[Article in Mathematics ArXiv]*Enriques Surfaces and jacobian elliptic K3 surfaces (with K. Hulek) **

Math. Z.**268**(2011), 1025-1056.

[Article in Mathematics ArXiv]*Lifts of projective congruence subgroups (with I. Kiming, H. Verrill)*

J. London Math. Soc. (2011)**83**(1), 96-120.

[Article in Mathematics ArXiv]*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]*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]*Lines on Fermat surfaces (with T. Shioda, R. van Luijk)*

Journal of Number Theory**130**(2010), 1939-1963.

[Article in Mathematics ArXiv]*K3 surfaces of Picard rank 20 over Q*

Algebra & Number Theory**4**(2010), no. 3, 335-356.

[Article in Mathematics ArXiv]*K3 surfaces with non-symplectic automorphism of 2-power order*

Journal of Algebra**323**(2010), 206-223.

[Article in Mathematics ArXiv]*CM newforms with rational coefficients*

Ramanujan Journal**19**(2009), 187-205.

[Article in Mathematics ArXiv]*Generalised Kummer constructions and Weil restrictions (with S. Cynk)*

Journal of Number Theory**129**(2009), 1965-1975.

[Article in Mathematics ArXiv]*Arithmetic of K3 surfaces*

Jahresbericht der DMV**111**(2009), 23-41.

[Article in Mathematics ArXiv]*Unirational Surfaces on the Noether Line (with C. Liedtke)*

Pacific J. Math.**239**(2009), 343-356.

[Article in Mathematics ArXiv]*Arithmetic of a singular K3 surface*

Michigan Math. J.**56**(2008), 513-527.

[Article in Mathematics ArXiv]*On Davenport-Stothers inequalities and elliptic surfaces in positive characteristic (with A. Schweizer)*

Quarterly J. Math.**59**(2008), 499-522.

[Article in Mathematics ArXiv]*Fields of definition of singular K3 surfaces*

Communications in Number Theory and Physics**1**, 2 (2007), 307-321.

[Article in Mathematics ArXiv]*An interesting elliptic surface over an elliptic curve (with T. Shioda)*

Proc. Jap. Acad.**83**, 3 (2007), 40-45.

[Article in Mathematics ArXiv]*Elliptic fibrations of some extremal K3 surfaces*

Rocky Mountain Journal of Mathematics**37**, 2 (2007), 609-652.

[Article in Mathematics ArXiv]*The maximal singular fibres of elliptic K3 surfaces**

Archiv der Mathematik**79**, 4 (2006), 309-319.

[Article in Mathematics ArXiv]*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]*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]*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]*New examples of modular rigid Calabi-Yau threefolds*

Collect. Math.**55**, 2 (2004), 219-228.

[Article in Mathematics ArXiv]## Books (authored/edited)

*Mordell-Weil lattices (with T. Shioda)*

to appear in Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge*Calabi-Yau Varieties: Arithmetic, Geometry and Physics (with R. Laza, N. Yui)*

Fields Institute Monographs, Vol.**34**, x + 547 p., Springer (2015)-
*Algebraic and Complex Geometry (with A. Frühbis-Krüger, R. Kloosterman)*

Springer PROMS**71**, xii + 319 p., Springer (2014) *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 StratenExplicit 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 PacettiMAGMA 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