19 Result(s)

Chapter

CY-Operators and L-Functions

This a write up of a talk given at the MATRIX conference at Creswick in 2017 (to be precise, on Friday, January 20, 2017). It reports on work in progress with P. Candelas and X. de la Ossa. The aim of that work i...

Duco van Straten in 2017 MATRIX Annals (2019)

Chapter

On a Theorem of Greuel and Steenbrink

A famous theorem of Greuel and Steenbrink states that the first Betti number of the Milnor fibre of a smoothing of a normal surface singularity vanishes. In this paper we prove a general theorem on the first B...

Duco van Straten in Singularities and Computer Algebra (2017)

Chapter and Conference Paper

Logarithmic Vector Fields and the Severi Strata in the Discriminant

The discriminant, D, in the base of a miniversal deformation of an irreducible plane curve singularity, is partitioned according to the genus of the (singular) fibre, or, equivalently, by the sum of the delta inv...

Paul Cadman, David Mond, Duco van Straten in Singularities in Geometry, Topology, Folia… (2017)

Article

Dwork congruences and reflexive polytopes

We show that the coefficients of the power series expansion of the principal period of a Laurent polynomial satisfy strong congruence properties. These congruences play key role in the explicit p-adic analytic co...

Kira Samol, Duco van Straten in Annales mathématiques du Québec (2015)

Chapter

Tree Singularities: Limits, Series and Stability

A tree singularity is a surface singularity that consists of smooth components, glued along smooth curves in the pattern of a tree. Such singularities naturally occur as degenerations of certain rational surfa...

Duco Van Straten in Deformations of Surface Singularities (2013)

Article

On the monodromy of the moduli space of Calabi–Yau threefolds coming from eight planes in \({\mathbb{P}^3}\)

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 Hermitian symmetric domains. In the p...

Ralf Gerkmann, Mao Sheng, Duco van Straten, Kang Zuo in Mathematische Annalen (2013)

Chapter

Calabi–Yau Conifold Expansions

We describe examples of computations of Picard–Fuchs operators for families of Calabi–Yau manifolds based on the expansion of a period near a conifold point. We find examples of operators without a point of ma...

Slawomir Cynk, Duco van Straten in Arithmetic and Geometry of K3 Surfaces and… (2013)

Article

Small resolutions and non-liftable Calabi-Yau threefolds

We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau threefolds. In particular, we construct a smooth projective Calabi-Yau threefo...

Sławomir Cynk, Duco van Straten in manuscripta mathematica (2009)

Article

Smoothing of quiver varieties

We show that Gorenstein singularities that are cones over singular Fano varieties provided by so-called flag quivers are smoothable in codimension three. Moreover, we give a precise characterization about the ...

Klaus Altmann, Duco van Straten in manuscripta mathematica (2009)

Chapter

Real Line Arrangements and Surfaces with Many Real Nodes

Sonja Breske, Oliver Labs, Duco van Straten in Geometric Modeling and Algebraic Geometry (2008)

Article

Rigid and Complete Intersection Lagrangian Singularities

In this article we prove a rigidity theorem for lagrangian singularities by studying the local cohomology of the lagrangian de Rham complex that was introduced in [SvS03]. The result can be applied to show the...

Christian Sevenheck, Duco van Straten in manuscripta mathematica (2004)

Article

Deformation of singular lagrangian subvarieties

We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. This cohomology turns out to be constr...

Christian Sevenheck, Duco van Straten in Mathematische Annalen (2003)

Chapter and Conference Paper

A Visual Introduction to Cubic Surfaces Using the Computer Software Spicy

At the end of the 19^th century geometers like Clebsch, Klein and Rodenberg constructed plaster models in order to get a visual impression of their surfaces, which are so beautiful from an abstract point of view. ...

Duco van Straten, Oliver Labs in Algebra, Geometry and Software Systems (2003)

Article

Mirror symmetry and toric degenerations of partial flag manifolds

Victor V. Batyrev, Ionuţ Ciocan-Fontanine, Bumsig Kim, Duco van Straten in Acta Mathematica (2000)

Article

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV _{1 ...}

Victor V. Batyrev, Duco van Straten in Communications in Mathematical Physics (1995)

Article

Extendability of holomorphic differential forms near isolated hypersurface singularities

Duco van Straten, Joseph Steenbrink in Abhandlungen aus dem Mathematischen Semina… (1985)