Matches in SemOpenAlex for { <https://semopenalex.org/work/W3006152009> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W3006152009 abstract "Apolarity is an important tool in commutative algebra and algebraic geometry which studies a form, $f$, by the action of polynomial differential operators on $f$. The quotient of all polynomial differential operators by those which annihilate $f$ is called the apolar algebra of $f$. In general, the apolar algebra of a form is useful for determining its Waring rank, which can be seen as the problem of decomposing the supersymmetric tensor, associated to the form, minimally as a sum of rank one supersymmetric tensors. In this article we study the apolar algebra of a product of linear forms, which generalizes the case of monomials and connects to the geometry of hyperplane arrangements. In the first part of the article we provide a bound on the Waring rank of a product of linear forms under certain genericity assumptions; for this we use the defining equations of so-called star configurations due to Geramita, Harbourne, and Migliore. In the second part of the article we use the computer algebra system Bertini, which operates by homotopy continuation methods, to solve certain rank equations for catalecticant matrices. Our computations suggest that, up to a change of variables, there are exactly six homogeneous polynomials of degree six in three variables which factor completely as a product of linear forms defining an irreducible multi-arrangement and whose apolar algebras have dimension six in degree three. As a consequence of these calculations, we find six cases of such forms with cactus rank six, five of which also have Waring rank six. Among these are products defining subarrangements of the braid and Hessian arrangements." @default.
- W3006152009 created "2020-02-24" @default.
- W3006152009 creator A5019600747 @default.
- W3006152009 creator A5078621088 @default.
- W3006152009 creator A5087962118 @default.
- W3006152009 date "2020-02-12" @default.
- W3006152009 modified "2023-09-27" @default.
- W3006152009 title "The apolar algebra of a product of linear forms" @default.
- W3006152009 cites W1820867527 @default.
- W3006152009 cites W2033395767 @default.
- W3006152009 cites W2064591878 @default.
- W3006152009 cites W2183937650 @default.
- W3006152009 cites W2900224119 @default.
- W3006152009 cites W2963432819 @default.
- W3006152009 cites W59564462 @default.
- W3006152009 cites W71831445 @default.
- W3006152009 hasPublicationYear "2020" @default.
- W3006152009 type Work @default.
- W3006152009 sameAs 3006152009 @default.
- W3006152009 citedByCount "0" @default.
- W3006152009 crossrefType "posted-content" @default.
- W3006152009 hasAuthorship W3006152009A5019600747 @default.
- W3006152009 hasAuthorship W3006152009A5078621088 @default.
- W3006152009 hasAuthorship W3006152009A5087962118 @default.
- W3006152009 hasConcept C101044782 @default.
- W3006152009 hasConcept C11252640 @default.
- W3006152009 hasConcept C114614502 @default.
- W3006152009 hasConcept C134306372 @default.
- W3006152009 hasConcept C136119220 @default.
- W3006152009 hasConcept C164226766 @default.
- W3006152009 hasConcept C17103678 @default.
- W3006152009 hasConcept C202444582 @default.
- W3006152009 hasConcept C2524010 @default.
- W3006152009 hasConcept C33923547 @default.
- W3006152009 hasConcept C51255310 @default.
- W3006152009 hasConcept C68363185 @default.
- W3006152009 hasConcept C68693459 @default.
- W3006152009 hasConcept C78313660 @default.
- W3006152009 hasConcept C90119067 @default.
- W3006152009 hasConcept C90673727 @default.
- W3006152009 hasConceptScore W3006152009C101044782 @default.
- W3006152009 hasConceptScore W3006152009C11252640 @default.
- W3006152009 hasConceptScore W3006152009C114614502 @default.
- W3006152009 hasConceptScore W3006152009C134306372 @default.
- W3006152009 hasConceptScore W3006152009C136119220 @default.
- W3006152009 hasConceptScore W3006152009C164226766 @default.
- W3006152009 hasConceptScore W3006152009C17103678 @default.
- W3006152009 hasConceptScore W3006152009C202444582 @default.
- W3006152009 hasConceptScore W3006152009C2524010 @default.
- W3006152009 hasConceptScore W3006152009C33923547 @default.
- W3006152009 hasConceptScore W3006152009C51255310 @default.
- W3006152009 hasConceptScore W3006152009C68363185 @default.
- W3006152009 hasConceptScore W3006152009C68693459 @default.
- W3006152009 hasConceptScore W3006152009C78313660 @default.
- W3006152009 hasConceptScore W3006152009C90119067 @default.
- W3006152009 hasConceptScore W3006152009C90673727 @default.
- W3006152009 hasLocation W30061520091 @default.
- W3006152009 hasOpenAccess W3006152009 @default.
- W3006152009 hasPrimaryLocation W30061520091 @default.
- W3006152009 hasRelatedWork W1950670036 @default.
- W3006152009 hasRelatedWork W1994176685 @default.
- W3006152009 hasRelatedWork W2039002646 @default.
- W3006152009 hasRelatedWork W2043540451 @default.
- W3006152009 hasRelatedWork W2054582539 @default.
- W3006152009 hasRelatedWork W2071704072 @default.
- W3006152009 hasRelatedWork W2076088986 @default.
- W3006152009 hasRelatedWork W2077428997 @default.
- W3006152009 hasRelatedWork W2085189628 @default.
- W3006152009 hasRelatedWork W2130942765 @default.
- W3006152009 hasRelatedWork W2226054218 @default.
- W3006152009 hasRelatedWork W2236401661 @default.
- W3006152009 hasRelatedWork W2308561958 @default.
- W3006152009 hasRelatedWork W2925709418 @default.
- W3006152009 hasRelatedWork W2953153220 @default.
- W3006152009 hasRelatedWork W2963695899 @default.
- W3006152009 hasRelatedWork W3006881177 @default.
- W3006152009 hasRelatedWork W3099792655 @default.
- W3006152009 hasRelatedWork W3166075240 @default.
- W3006152009 hasRelatedWork W84463221 @default.
- W3006152009 isParatext "false" @default.
- W3006152009 isRetracted "false" @default.
- W3006152009 magId "3006152009" @default.
- W3006152009 workType "article" @default.