93 citations · 392 across the 21 of their papers we have counts for
25 papers
The platonic elliptic surfaces
Nutsa Gegelia, Duco van Straten
We construct certain special rational elliptic surfaces with four reduced singular fibres that are naturally attached to the platonic solids and belong to a group of surfaces compl…
The Hamiltonian Normal Form
Mauricio Garay, Duco van Straten
An important step in the proof of the Herman invariant tori conjecture was the introduction of a normal form with poles along the resonance loci, replacing the Birkhoff normal form…
Fixed point theorems for small divisors problems
Mauricio Garay, Duco van Straten
In the seventies', Zehnder found a Nash-Moser type implicit function theorem in the analytic set-up. This theorem has found many applications in dynamical systems although its appl…
A new class of Borel monogenic functions
Mauricio Garay, Duco van Straten
Spaces of quasi-analytic classes are defined by the existence and uniqueness of Taylor expansions, which are not necessarily convergent. First examples were given by Borel in his t…
Non degenerate Birkhoff functions
Mauricio Garay, Duco van Straten
It is known after the works of Mahler, Kleinbock, Margulis, Sprindžuk and others that very well approximated numbers on a manifold form a zero measure set, assuming non-degeneracy…
A remarkable eelliptic curve
Duco van Straten
We describe a system of plane algebraic curves defined over \Z, attached naturally to the exponential function. On of these is a remarkable curve of degree 6 that has genus equal t…
A -algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals
Pascal Prass, Fabian R. Lux, Emil Prodan +2
Understanding the interaction of real- and reciprocal space topology in skyrmion crystals is an open problem. We approach it from the viewpoint of -algebras and calculate a…
A hyperelliptic saga on a generating function of the squares of Legendre polynomials
Mark van Hoeij, Duco van Straten, Wadim Zudilin
We decompose the generating function of the squares of Legendre polynomials as a product of periods of hyperelliptic curves. These periods…
A Category of Banach Space Functors
Mauricio Garay, Duco van Straten
We introduce a sheaf theoretic viewpoint on functional analysis designed for infinite dimensional Lie group actions. We develop functional calculus for Banach valued functors and,…
The Herman invariant tori conjecture
Mauricio Garay, Duco van Straten
We study a new type of normal form at a critical point of an analytic Hamiltonian. Under a Bruno condition on the frequency, we prove a convergence statement to the normal form. Us…
Calabi--Yau Operators
Duco van Straten
Motivated by mirror symmetry of one-parameter models, an interesting class of Fuchsian differential operators can be singled out, the so-called Calabi--Yau operators, introduced by…
Logarithmic vector fields and the Severi strata in the discriminant
Paul Cadman, David Mond, Duco van Straten
The discriminant, , in the base of a miniversal deformation of an irreducible plane curve singularity, is partitioned according to the genus of the (singular) fibre, or, equival…
Some monodromy groups of finite index in
Jörg Hofmann, Duco van Straten
We determine the index of five of the hypergeometric Calabi-Yau operators that have finite index in and in two cases give a complete description of the monod…
Resurgent Deformation Quantisation
Mauricio Garay, Axel de Goursac, Duco van Straten
We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. In particular, we exhibit an integral formula for the product of resurg…
Twisted cubics on cubic fourfolds
Christian Lehn, Manfred Lehn, Christoph Sorger +1
We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space M_3(Y) of twisted cubics on…
An abelian surface with (1,6)-polarisation
Michael Semmel, Duco van Straten
We use the method of Adler-van Moerbeke and Vanhaecke to show that the general fibre of the hamiltonian system of Dorizzi, Grammaticos and Ramani completes to a (1, 6)-polarised ab…
Gorenstein-duality for one-dimensional almost complete intersections-with an application to non-isolated real singularities
Duco van Straten, Thorsten Warmt
We give a generalization of the duality of a zero-dimensional complete intersection to the case of one-dimensional almost complete intersections, which results in a {\em Gorenstein…
An Index Theorem for Modules on a Hypersurface Singularity
Ragnar-Olaf Buchweitz, Duco van Straten
A topological interpretation of Hochster's Theta pairing of two modules on a hypersurface ring is given in terms of linking numbers. This generalizes results of M. Hochster and pro…
On the monodromy of the moduli space of Calabi-Yau threefolds coming from eight planes in
Ralf Gerkmann, Mao Sheng, Duco van Straten +1
It is a fundamental problem in geometry to decide which moduli spaces of polarized algebraic varieties are embedded by their period maps as Zariski open subsets of locally Hermitia…
Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds
Pedro Luis del Angel, Stefan Müller-Stach, Duco van Straten +1
We use -Higgs cohomology to determine the Hodge numbers of the parabolic cohomology $H^1(\bar S, j_*\V)$, where the local system $\V$ arises from the third primitive cohomolog…
Tables of Calabi--Yau equations
Gert Almkvist, Christian van Enckevort, Duco van Straten +1
The main part of this paper is a big table containing what we believe to be a complete list of all fourth order equations of Calabi--Yau type known so far. In the text preceding th…
Infinitesimal deformations of double covers of smooth algebraic varieties
Slawomir Cynk, Duco van Straten
The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deform…
Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians
Victor V. Batyrev, Ionunt Ciocan-Fontanine, Bumsig Kim +1
In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of…
Euler number of the compactified Jacobian and multiplicity of rational curves
Barbara Fantechi, Lothar Göttsche, Duco van Straten
We show that the Euler number of the compactified Jacobian of a rational curve with locally planar singularities is equal to the multiplicity of the -constant stratum in the…