Power Sums, Gorenstein Algebras, and Determinantal Loci

By A. Iarrobino, V. Kanev. 2000

607 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8889952e9573170a6e729bc2d8c768a8dcb9eee8

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Citations in the corpus

Multigraded Castelnuovo-Mumford Regularity (2003, background): “Although the precise definition may seem rather technical, its value in bounding the degree of syzygies [20], [13] and constructing Hilbert schemes [18], [26] has established that regularity is an indispensable tool in both fields.”
Isomorphism classes of short Gorenstein local rings via Macaulay's inverse system (2012, background): “Notice that the Proposition 2.2 result extends [17, Appendix A] or [11, Section C, Proposition 17] to the nonhomogeneous case.”
On generic identifiability of symmetric tensors of subgeneric rank (2015, background): “ decomposition, which expresses a symmetric tensor as a sum of powers of linear forms. Precisely, every form f ∈ SdCn+1 has a minimal expression (1) f = Xr i=1 ld i , where li ∈ Cn+1 are linear forms [23]; the minimal number of summands r is called the symmetric rank of f, since in the correspondenc”
The equations defining blowup algebras of height three Gorenstein ideals (2015, background): “n ideal; see Theorem 9.1 and Remark 9.2. Height three Gorenstein ideals have been studied extensively, and there is a vast literature dealing with the various aspects of the subject; see for instance [52, 8, 20, 41, 3, 42, 16, 1, 17, 22, 45, 34, 49, 43, 12, 24, 4, 33]. Though it may be impossible to”
Waring Decompositions of Monomials (2012, background): “nd these cases it is a diﬃcult problem to determine or even to give decent bounds on R(F), even for seemingly simple polynomials such as monomials. For much more on this topic, including history, see [IK99] and more recently [Rez10]. Regarding monomials, the paper [LT10] found R(xyz) = 4, R(xyzw) = ”
Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers (2001, background): “IfX ;Y Pn are geom etrically linked and reg(X [ Y ) 2 reg(X ) then (foralli) TorRi (R=(IX + IY );K ) = Tor R i (R=IX ;K ) Tor R i 1(K X ;K )( reg(X [ Y ) c+ n + 2) where K X := Ext c R(R=IX ;R)( n 1)denotesthe canonicalm odule ofX .”
Equations for secant varieties of Veronese and other varieties (2011, methodology): “Case Equations Cuts out References σr (v2(P n)) Size r + 1 minors Ideal Classical σr (vd (P 1)) Size r + 1 minors of any φs,d−s Ideal Gundelfinger, [25]”
Varieties with minimal secant degree and linear systems of maximal dimension on surfaces (2004, background): “olation problems, rank tensor computations and canonical forms, expressions of polynomials as sums of powers and Waring type problems, algebraic statistics etc. (see, for instance, [C], [CGG], [GSS], [IK]). Going back to projective algebraic geometry, let us mention the ﬁrst basic example of a prope”