8 citations · 14 across the 11 of their papers we have counts for
13 papers
Closedness of bounded strength and partition rank loci
Benjamin Baily, Alessandro Danelon
We show the existence of a quartic form of strength in the closure of the strength at most locus, answering a question of Ballico--Bik--Oneto--Ventura in the negative. In t…
The fundamental theorems of invariant theory for linearly oligomorphic groups
Alessandro Danelon, Andrew Snowden
In recent work, Harman and the second author introduced some new infinite dimensional algebraic groups that generalize the classical groups. In this paper, we establish versions of…
The singular locus of a GL-variety
Christopher Heng Chiu, Alessandro Danelon, Andrew Snowden
A -variety is a (typically) infinite dimensional variety equipped with an action of the infinite general linear group. In recent work of the first two authors with…
Topological noetherianity for powers of algebraic representations
Alessandro Danelon
Powers of a polynomial -representation are topologically Noetherian under the action of . We extend this result to p…
Balanced player arrangement in rotating court games
Alessandro Danelon
Consider a game involving a team with players, of which wear shirts marked with a letter , while the others with a letter , and such that only people play, while…
A remark on automorphisms of tensor spaces
Alessandro Danelon, Andrew Snowden
A tensor space is a vector space equipped with a finite collection of multi-linear forms. In recent years, a rich theory of infinite dimensional tensor spaces has emerged. In this…
Singular loci in varieties of tensors
Christopher Chiu, Alessandro Danelon, Jan Draisma
A Vec-variety is a suitable functor from finite-dimensional vector spaces to finite-dimensional varieties. Most varieties in the geometry of tensors, e.g. the variety of d-way tens…
Biquadratic spaces of length two
Alessandro Danelon, Andrew Snowden
A tensor space is a vector space equipped with a finite collection of multilinear forms. The length of a tensor space is its length as a representation of its symmetry group. Infin…
Sym-Noetherianity for powers of GL-varieties
Christopher H. Chiu, Alessandro Danelon, Jan Draisma +2
Much recent literature concerns finiteness properties of infinite-dimensional algebraic varieties equipped with an action of the infinite symmetric group, or of the infinite genera…
Isogeny classes of cubic spaces
Arthur Bik, Alessandro Danelon, Andrew Snowden
A cubic space is a vector space equipped with a symmetric trilinear form. Two cubic spaces are isogeneous if each embeds into the other. A cubic space is non-degenerate if its form…
The enumerative geometry of cubic hypersurfaces: point and line conditions
Mara Belotti, Alessandro Danelon, Claudia Fevola +1
In order to count the number of smooth cubic hypersurfaces tangent to a prescribed number of lines and passing through a given number of points, we construct a compactification of…
Universality of high-strength tensors
Arthur Bik, Alessandro Danelon, Jan Draisma +1
A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given p…
Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum
Arthur Bik, Alessandro Danelon, Jan Draisma
In a previous paper, the third author proved that finite-degree polynomial functors over infinite fields are topologically Noetherian. In this paper, we prove that the same holds f…