Related papers: Syzygy algebras for the Segre embeddings

This paper studies syzygies of curves that have been embedded in projective space by line bundles of large degree. The proofs take advantage of the relationship between syzygies and spaces of section of vector bundles associated to the…

Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract…

We prove that there is no g for which the canonical embedding of a general curve of genus g lies on the Segre embedding of any product of three or more projective spaces.

Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated . The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

By adapting methods of Ein-Erman-Lazarsfeld, we prove an analogue of the Ein-Lazarsfeld result on asymptotic syzygies for Veronese embeddings, in the setting of weighted projective spaces of the form $\mathbb{P}(1^n,2)$.

We study a class obtained from the Segre class $s(Z,Y)$ of an embedding of schemes by incorporating the datum of a line bundle on $Z$. This class satisfies basic properties analogous to the ordinary Segre class, but leads to remarkably…

Invariant notions of a class of Segre varieties $\Segrem(2)$ of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a…

For an algebraically closed field $k$ of characteristic zero and a linear algebraic $k$-group $G$, it is well known that every affine $G$-variety admits a $G$-equivariant closed embedding into a finite-dimensional $G$-module. Such an…

This paper studies the asymptotic behavior of the syzygies of a smooth projective variety X as the positivity of the embedding line bundle grows. We prove that as least as far as grading is concerned, the minimal resolution of the ideal of…

We study the Virasoro constraints for moduli spaces of representations of quiver with relations by Joyce's vertex algebras. Using the framed Virasoro constraints, we construct a representation of half of the Virasoro algebra on the…

The syzygies of the d-th Veronese embedding of $\mathbb P(V)$ are functors of the complex vector space V. From a certain perspective, we show that as d grows, their Schur functor decomposition is very rich whenever they are not zero. This…

Let $(X,r_X)$ and $(Y,r_Y)$ be finite nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation, and let $A_X = A(\textbf{k}, X, r_X)$ and $A_Y= A(\textbf{k}, Y, r_Y)$ be their quadratic Yang-Baxter algebras over a field…

Two-dimensional linear spaces of symmetric matrices are classified by Segre symbols. After reviewing known facts from linear algebra and projective geometry, we address new questions motivated by algebraic statistics and optimization. We…

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1,1...1], [21...1], [31\ldots 1],…

An embedding of a graph on a translation surface is said to be \emph{systolic} if each vertex of the graph corresponds to a singular point (or marked point) and each edge corresponds to a shortest saddle connection on the translation…

We provide a characterization of homogeneous spaces under a reductive group scheme such that the geometric stabilizers are maximal tori. The quasi-split case over a semilocal base is of special interest and permits to answer a question…

We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i.) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii.)…

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning,…

The main result of this paper is the following: let d be a natural number >= 3; the line bundle O(1,...,1) on the product of d copies of the projective line P^1 satisfies Property N_p of Green-Lazarsfeld if and only if p <= 3.