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- Victor V. Batyrev, Duco van Straten
- 1995

We formulate general conjectures about the relationship between the A-model connection on the cohomology of a d-dimensional Calabi-Yau complete intersection V of r hypersurfaces V1, . . . , Vr in a toric variety PΣ and the system of differential operators annihilating the special generalized hypergeometric function Φ0 depending on the fan Σ. In this… (More)

- Victor V. Batyrev, Duco van Straten
- 1997

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 rational curves on complete intersection Calabi-Yau 3-folds in Grassmannians. Using a natural degeneration of Grassmannians G(k, n) to some Gorenstein toric Fano varieties P (k,… (More)

- T. de Jong, D. van Straten
- 2007

In this paper we describe the deformation theory of sandwiched sin-gularities in terms of-constant deformations of plane curves, and a divisor of points on it. This leads to an immediate understanding of the smoothings of sandwiched singularities in terms of pictures: certain conngurations of points and curves with only d-fold points in the plane. The… (More)

- Victor V. Batyrev, Bumsig Kim, Duco van Straten
- 2008

In this paper we propose and discuss a mirror construction for complete intersections in partial flag manifolds F (n1, . . . , nl, n). This construction includes our previous mirror construction for complete intersection in Grassmannians and the mirror construction of Givental for complete flag manifolds. The key idea of our construction is a degeneration… (More)

- Gert Almkvist, Christian van Enckevort, Duco van Straten, Wadim Zudilin
- 2005

The main part of this paper is a big table (see Appendix A) 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 the tables we explain what a differential equation of Calabi–Yau type is and we briefly discuss how we found these equations. We also describe an electronic version… (More)

- DUCO VAN STRATEN
- 2003

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. This research was inspired by the analysis of Calabi–Yau manifolds that arise as smooth models of double covers of P branched along singular octic surfaces ([4, 3]). It is of considerable interest to determine the… (More)

- Kira Samol, Duco van Straten, D. van Straten
- 2008

We describe a variation of Dworks unit-root method to determine the degree four Frobenius polynomial for members of a 1-modulus Calabi-Yau family over P1 in terms of the holomorphic period near a point of maximal unipotent monodromy. The method is illustrated on a couple of examples from the list [3]. For singular points we find that the Frobenius… (More)

We provide certain unusual generalizations of Clausen’s and Orr’s theorems for solutions of fourth-order and fifth-order generalized hypergeometric equations. As an application, we present several examples of algebraic transformations of Calabi–Yau differential equations.

- E. IZADI, D. VAN STRATEN
- 1995

Let A be a principally polarized abelian variety of dimension four and let Θ ⊂ A be a symmetric theta-divisor, which we assume to be smooth. Using the Hodge structure on H(Θ) we associate to A two abelian subvarieties J(K) ⊂ J(H) of the intermediate jacobian J(Θ) of Θ of dimensions five and nine respectively. We show that J(H) is generated by the image… (More)