The Barth quintic surface has Picard number 41 (with S. Rams)
Submitted
[Article
in Mathematics ArXiv]
Two moduli spaces of abelian fourfolds with an automorphism of order five
(with Bert van Geemen)
Submitted
[Article
in Mathematics ArXiv]
Modularity of the Consani-Scholten quintic (with Luis Dieulefait
and
Ariel Pacetti)
Submitted
[Article
in Mathematics ArXiv]
Modular forms and K3 surfaces (with N. D. Elkies)
Submitted
[Article
in Mathematics ArXiv]
Two lectures on the arithmetic of K3 surfaces
To appear in Fields Institute Communications
[Article
in Mathematics ArXiv]
Sandwich theorems for Shioda-Inose structures
To appear in Izvestiya Mat.
[Article
in Mathematics ArXiv]
Enriques surfaces - Brauer groups and Kummer structures
(with Alice Garbagnati)
To appear in Michigan Math. Journal
[Article
in Mathematics ArXiv]
On the uniqueness of K3 surfaces with maximal singular fibre
(with
A. Schweizer)
To appear in Annales Institut Fourier
[Article
in Mathematics ArXiv]
Arithmetic of singular Enriques Surfaces (with K. Hulek)
To appear in Algebra & Number Theory
[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]
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
[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.