Noncommutative algebraic geometry: From pi-algebras to quantum groups.
Noncommutative compact manifolds constructed from quivers.
Noncommutative del Pezzo surfaces and Calabi-Yau algebras
The hypersurface in with an isolated quasi-homogeneous elliptic singularity of type , has a natural Poisson structure. We show that the family of del Pezzo surfaces of the corresponding type provides a semiuniversal Poisson deformation of that Poisson structure. We also construct a deformation-quantization of the coordinate ring of such a del Pezzo surface. To this end, we first deform the polynomial algebra to a noncommutative algebra with generators and the following 3 relations labelled...
Noncommutative geometry and the difraction one dimensional network.
Non-commutative Hodge structures
This article gives a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizable Hodge structure on the punctured affine line, like the Gauss-Manin systems of a proper or tame algebraic function on a smooth quasi-projective variety. Variations of non-commutative Hodge structures often occur on the tangent bundle of Frobenius manifolds, giving rise to a tt* geometry.
Noncommutative Local Algebra.
Noncommutative numerical motives, Tannakian structures, and motivic Galois groups
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined symmetric...
Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture
Non-conservative function fields of genus (p + 1) /2.
Non-conservative plane quartic curves in characteristic five.
Non-deformability of entire curves in projective hypersurfaces of high degree
In this article, we prove that there does not exist a family of maximal rank of entire curves in the universal family of hypersurfaces of degree in the complex projective space . This can be seen as a weak version of the Kobayashi conjecture asserting that a general projective hypersurface of high degree is hyperbolic in the sense of Kobayashi.
Nondegenerate surfaces of degree n+3 in PnC.
Non-embeddable -convex manifolds
We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable -convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type . To this end we study small resolutions of -singularities.
Non-existence of points rational over number fields on Shimura curves
Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
Nonflat deformations of modules and isolated singularities.
Non-free Projective Modules Over IH[X, Y] and Stable Bundles Over IP2(...).
Non-hyperelliptic fibrations of small genus and certain irregular canonical surfaces
Nonisomorphic algebraic models of a smooth manifold.
Nonlinear Equivariant Automorphisms.
Non-normal del Pezzo durfaces and Fano threefolds of the first kind.