International Conference. A.G.Khovanskii – “Newton polyhedra and affine algebraic varieties”
International Conference, dedicated to the 75th birthday of Sabir M. Gusein-Zade 19.06.25 A. G. Khovanskii (Toronto, Canada) Newton polyhedra and affine algebraic varieties Let X be a subset of C^n defined by a system of generic polynomial equations P_1 = ... = P_k = 0 with given Newton polyhedra. We compute the number of irreducible components in X of different dimensions and the multiplicity of irreducible components of dimension n - k. In particular, when k = n we compute the number of isolated points in X of different multiplicities. Unlike varieties in the torus (C^*)^n, defined similarly, X may have isolated points of arbitrary multiplicity and irreducible components of arbitrary dimension. We also generalize these results to subvarieties in a smooth (possibly incomplete) n-dimensional toric variety V defined as the common null set of several sections of (possibly distinct) invariant line bundles over V, assuming that these sections are generic with respect to given Newton polyhedra. General information The conference will be held in the Faculty of Mathematics of the HSE University (Usacheva str. 6, Moscow). Dates: 16 - 20 June 2025 Organizers: A. Buryak, V. Medvedev, A. Skripchenko More information: https://math.hse.ru/modern_aspects_singularity_theory25/ https://mccme.ru/ru/modern_aspects_singularity_theory2025/
International Conference, dedicated to the 75th birthday of Sabir M. Gusein-Zade 19.06.25 A. G. Khovanskii (Toronto, Canada) Newton polyhedra and affine algebraic varieties Let X be a subset of C^n defined by a system of generic polynomial equations P_1 = ... = P_k = 0 with given Newton polyhedra. We compute the number of irreducible components in X of different dimensions and the multiplicity of irreducible components of dimension n - k. In particular, when k = n we compute the number of isolated points in X of different multiplicities. Unlike varieties in the torus (C^*)^n, defined similarly, X may have isolated points of arbitrary multiplicity and irreducible components of arbitrary dimension. We also generalize these results to subvarieties in a smooth (possibly incomplete) n-dimensional toric variety V defined as the common null set of several sections of (possibly distinct) invariant line bundles over V, assuming that these sections are generic with respect to given Newton polyhedra. General information The conference will be held in the Faculty of Mathematics of the HSE University (Usacheva str. 6, Moscow). Dates: 16 - 20 June 2025 Organizers: A. Buryak, V. Medvedev, A. Skripchenko More information: https://math.hse.ru/modern_aspects_singularity_theory25/ https://mccme.ru/ru/modern_aspects_singularity_theory2025/