Seminars: K. V. Loginov, Polynomials with integral coefficients, equivalent to a given polynomial (after Ja. Kollar)

SEMINARS


Iskovskikh Seminar September 21, 2017 18:00, Moscow, Steklov Mathematical Institute, room 530

Polynomials with integral coefficients, equivalent to a given polynomial (after Ja. Kollar) K. V. Loginov National Research University "Higher School of Economics" (HSE), Moscow
Abstract: Consider the following problem: given a homogeneous polynomial $f(x_0,\ldots,x_n)$ with rational coefficients, construct a polynomial $F(x_0,\ldots,x_n)$ with integral coefficients which is “equivalent” to f and as “simple” as possible. The exact definitions and the solution to this problems are given in terms of stability conditions coming from Geometric invariant theory. As an application we discuss the good models of the cubic surface fibrations.