122 citations · 901 across the 71 of their papers we have counts for
17 papers · 1 filter
Cohomology of flag supervarieties and resolutions of determinantal ideals. II
Steven V Sam, Andrew Snowden
We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular…
Uniformity for limits of tensors
Arthur Bik, Jan Draisma, Rob Eggermont +1
There are many notions of rank in multilinear algebra: tensor rank, partition rank, slice rank, and strength (or Schmidt rank) are a few examples. Typically the rank locus…
Cohomology of flag supervarieties and resolutions of determinantal ideals
Steven V Sam, Andrew Snowden
We study the coherent cohomology of generalized flag supervarieties. Our main observation is that these groups are closely related to the free resolutions of (certain generalizatio…
The geometry of polynomial representations
Arthur Bik, Jan Draisma, Rob H. Eggermont +1
We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms…
Symmetric subvarieties of infinite affine space
Rohit Nagpal, Andrew Snowden
We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these va…
Strength and Hartshorne's Conjecture in high degree
Daniel Erman, Steven V Sam, Andrew Snowden
Hartshorne conjectured that a smooth, codimension c subvariety of n-dimensional projective space must be a complete intersection, whenever c is less than n/3. We prove this in the…
An equivariant Hilbert basis theorem
Daniel Erman, Steven V Sam, Andrew Snowden
We prove a version of the Hilbert basis theorem in the setting of equivariant algebraic geometry: given a group G acting on a finite type morphism of schemes X -> S, if S is topolo…
Topological noetherianity for cubic polynomials
Harm Derksen, Rob H. Eggermont, Andrew Snowden
Let be the space of complex cubic polynomials in infinitely many variables. We show that this space is -noetherian, meaning that an…
Finiteness of K3 surfaces and the Tate conjecture
Max Lieblich, Davesh Maulik, Andrew Snowden
Given a finite field k of characteristic at least 5, we show that the Tate conjecture holds for K3 surfaces defined over the algebraic closure of k if and only if there are only fi…
The geometry of eight points in projective space: Representation theory, Lie theory, dualities
Benjamin Howard, John Millson, Andrew Snowden +1
This paper deals with the geometry of the space (GIT quotient) M_8 of 8 points in P^1, and the Gale-quotient N'_8 of the GIT quotient of 8 points in P^3. The space M_8 comes with a…
Syzygies of Segre embeddings and Delta-modules
Andrew Snowden
We study syzygies of the Segre embedding of P(V_1) x ... x P(V_n), and prove two finiteness results. First, for fixed p but varying n and V_i, there is a finite list of "master p-s…
The ideal of relations for the ring of invariants of n points on the line
Ben Howard, John Millson, Andrew Snowden +1
The study of the projective coordinate ring of the (geometric invariant theory) moduli space of n ordered points on P^1 up to automorphisms began with Kempe in 1894, who proved tha…
The relations among invariants of points on the projective line
Ben Howard, John Millson, Andrew Snowden +1
We consider the ring of invariants of n points on the projective line. The space (P^1)^n // PGL_2 is perhaps the first nontrivial example of a Geometry Invariant Theory quotient. T…
The ring of projective invariants of eight points on the line via representation theory
Ben Howard, John Millson, Andrew Snowden +1
The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V, where V is a fourteen-dimensional representation of S_8, by an idea…
A description of the outer automorphism of S_6, and the invariants of six points in projective space
Ben Howard, John Millson, Andrew Snowden +1
We use a simple description of the outer automorphism of S_6 to cleanly describe the invariant theory of six points in P^1, P^2, and P^3.
The moduli space of n points on the line is cut out by simple quadrics when n is not six
Benjamin Howard, John Millson, Andrew Snowden +1
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence…
The projective invariants of ordered points on the line
Benjamin J. Howard, John Millson, Andrew Snowden +1
The space of n (ordered) points on the projective line, modulo automorphisms of the line, is one of the most important and classical examples of an invariant theory quotient, and i…