We prove that for each natural number k, the k-th secant variety of any Grassmannian is defined in bounded degree independent of the Grassmannian. These secant varieties are special cases of certain families of varieties, called Plücker varieties. The main result will be shown by considering limits of Plücker varieties and equivariant Noetherianity. The talk is based on the paper of Jan Draisma and Rob Eggermont with the same title.
We prove that for each natural number k, the k-th secant variety of any Grassmannian is defined in bounded degree independent of the Grassmannian. These secant varieties are special cases of certain families of varieties, called Plücker varieties. The main result will be shown by considering limits of Plücker varieties and equivariant Noetherianity. The talk is based on the paper of Jan Draisma and Rob Eggermont with the same title.
We prove that for each natural number k, the k-th secant variety of any Grassmannian is defined in bounded degree independent of the Grassmannian. These secant varieties are special cases of certain families of varieties, called Plücker varieties. The main result will be shown by considering limits of Plücker varieties and equivariant Noetherianity. The talk is based on the paper of Jan Draisma and Rob Eggermont with the same title.
We generalize the results of last week to so-called Abelian tree models. These are families of algebraic varieties, inspired by Markov processes on tress - more precisely phylogenetics. The talk is based on the paper of Jan Draisma and Rob Eggermont with the same title, JEMS 17, 711-738.
We generalize the results of last week to so-called Abelian tree models. These are families of algebraic varieties, inspired by Markov processes on tress - more precisely phylogenetics. The talk is based on the paper of Jan Draisma and Rob Eggermont with the same title, JEMS 17, 711-738.
We will present an article by Jan Draisma and Jochen Kuttler where they prove that for each k there exists an upper bound d=d(k) such that tensors of border rank at most k are defined by the vanishing of polynomials of degree at most d, regardless of the dimension of the tensor and regardless of its sizes in each dimension. The proofs are based on the methods introduced in the previous session of the reading group: It involves passing to an infinite-dimensional limit of tensor powers of a vector space and exploiting the symmetries of this limit in a crucial way.
In this talk, we will follow the paper “Noetherianity up to Symmetry” (Combinatorial Algebraic Geometry Volume 2108 of the series Lecture Notes in Mathematics, pp. 33-61) by Jan Draisma. We will discuss Noetherianity up to the action of a monoid in the setting of infinite-dimensional algebraic geometry. Many of the classical algebraic varieties come naturally in families. The equations of all varieties in these families have remarkably the same structure. The notion of equivariant Noetherianity encodes and explains such a behaviour. We will discuss some examples and applications from the cited paper.
