If X̃ is a Calabi–Yau threefold defined over Q, and p is a good prime (i.e., a prime such that the reduction of X̃ mod p is nonsingular) then the map Frob∗p : H i ét(X̃,Ql) −→ H i ét(X̃,Ql) on l–adic cohomology induced by the geometric Frobenius morphism gives rise to l–adic Galois representations ρl,i : Gal(Q/Q) −→ GLbi(Ql). If a Calabi–Yau threefold X̃ is rigid (i.e., h(X̃) = 0 or equivalently b(X̃)...

In this article, we prove that a free divisor in a three dimensional complex manifold must be Euler homogeneous in a strong sense if the cohomology of its complement is the hypercohomology of its logarithmic differential forms. F.J. Calderón–Moreno et al. [CMNC02] conjectured this implication in all dimensions and proved it in dimension two. We prove a theorem which describes in all dimensions ...

Barnouin-Jha, C. Honda, R. Nakamura , A. M. Nakamura, H. Demura, T. Michikami, M. Ishiguro, T. Hashimoto, T. Kubota, and J. Saito, Graduate School of Science and Technology, Kobe University, 1-1 Rokkodai, Kobe, Hyogo, 678-8501, Japan ([email protected]), Applied Physics Laboratory, The Johns Hopkins University, Institute of Space and Astronautical Sciences, Japan Aerospace Exploration Agenc...

We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is K(n, 1 ). These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is discussed as well. I. Definitions and ...

We propose alternative discriminant measures for selecting the best basis among a large collection of orthonormal bases for classi cation purposes. A generalization of the Local Discriminant Basis Algorithm of Saito and Coifman is constructed. The success of these new methods is evaluated and compared to earlier methods in experiments.

Abstract We associate a complete intersection singularity to graded matrix factorization of size two polynomial in three variables. show that we get an inverse the reduction singularities considered by C. T. Wall. study this for full strongly exceptional collections triangulated category factorizations constructed H. Kajiura, K. Saito, and second author.