Related papers: Waring loci and the Strassen conjecture

In 2005 Wolfgang Willems put forward a conjecture proposing a lower bound for the sum of squares of the degrees of the irreducible $p$-Brauer characters of a finite group $G$. We prove this conjecture for the prime $p=2$. For this we rely…

Given a closed subvariety X in a projective space, the rank with respect to X of a point p in this projective space is the least integer r such that p lies in the linear span of some r points of X. Let W_k be the closure of the set of…

Waring problem for forms is important and classical in mathematics. It has been widely investigated because of its wide applications in several areas. In this paper, we consider the Waring problem for binary forms with complex coefficients.…

The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…

The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial $p$ of degree $d$ as a finite sum of $d$-{th} powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any…

We establish a connection between properties of partially symmetric tensors (i.e. tensors associated to linear systems of quadric hypersurfaces) and the geometry of some related loci, generalization of the Weddle loci introduced in…

For any irreducible real reflection group $W$ with Coxeter number $h$, Armstrong, Reiner, and the author introduced a pair of $W \times \ZZ_h$-modules which deserve to be called {\sf $W$-parking spaces} which generalize the type A notion of…

We discuss an approach to the secant non-defectivity of the varieties parametrizing $k$-th powers of forms of degree $d$. It employs a Terracini type argument along with certain degeneration arguments, some of which are based on toric…

We develop a theory of \emph{reduced} Gromov-Witten and stable pair invariants of surfaces and their canonical bundles. We show that classical Severi degrees are special cases of these invariants. This proves a special case of the MNOP…

In this paper we compute the Waring rank of any polynomial of the form F=M_1+...+M_r, where the M_i are pairwise coprime monomials, i.e., GCD(M_i,M_j)=1 for i not j. In particular, we determine the Waring rank of any monomial. As an…

Grothendieck's standard conjecture of Lefschetz type has two main forms: the weak form $C$ and the strong form $B$. The weak form is known for varieties over finite fields as a consequence of the proof of the Weil conjectures. This suggests…

We formulate and prove examples of a conjecture which describes the W-algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine…

We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We translate the problem into a question about closed…

The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…

We prove that the singular locus of the commuting variety of a noncommutative reductive Lie algebra is contained in the irregular locus and we compute the codimension of the latter. We prove that one of the irreducible components of the…

In this note, we introduce and study position space Feynman quadrics that are the loci of divergences of the position space Feynman integrals for Euclidean massless scalar quantum field theories. We prove that the Feynman quadrics define…

Combining a selection of tools from modern algebraic geometry, representation theory, the classical invariant theory of binary forms, together with explicit calculations with hypergeometric series and Feynman diagrams, we obtain the…

In this paper, we study the real and the complex Waring rank of reducible cubic forms. In particular, we compute the complex rank of all reducible cubic forms. In the real case, for all reducible cubics, we either compute or bound the real…

On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $\mathbb C^*$ action with…

We determine the Waring ranks of all sextic binary forms with complex coefficients using a Geometric Invariant Theory approach. Using the five basic invariants for sextic binary forms, our results give a rapid method to determine the Waring…