Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

Eastwood, Michael; Isaev, Alexander

doi:10.1007/978-3-319-09804-3_7

Cited by 6 publications

(8 citation statements)

References 15 publications

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“…This proves (11). Finally, if f is homogeneous then g + f is equal to the span tdf(h) | h ∈ g + f by Proposition 2.20, and the last claim follows.…”

Section: Proposition 33 Let F ∈ P Then the Top Degree Form Of Everymentioning

confidence: 51%

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Classifying local Artinian Gorenstein algebras

Jelisiejew

2016

Collect. Math.

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The classification of local Artinian Gorenstein algebras is equivalent to the study of orbits of a certain non-reductive group action on a polynomial ring. We give an explicit formula for the orbits and their tangent spaces. We apply our technique to analyse when an algebra is isomorphic to its associated graded algebra. We classify algebras with Hilbert function (1, 3, 3, 3, 1), obtaining finitely many isomorphism types, and those with Hilbert function (1, 2, 2, 2, 1, 1, 1). We consider fields of arbitrary, large enough, characteristic.

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“…This proves (11). Finally, if f is homogeneous then g + f is equal to the span tdf(h) | h ∈ g + f by Proposition 2.20, and the last claim follows.…”

Section: Proposition 33 Let F ∈ P Then the Top Degree Form Of Everymentioning

confidence: 51%

“…The results usually rest on additional assumptions: small length [5,[7][8][9]37] or being a codimension two complete intersection [3,15,18]. See also [11,12,20,26] for other approaches.…”

Section: Introductionmentioning

confidence: 99%

Classifying local Artinian Gorenstein algebras

Jelisiejew

2016

Collect. Math.

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“…First, the morphism A is an SL(n)-equivariant locally closed immersion by [2, § 2.5], and so is stabilizer preserving. This proves the equivalence (5) ⇐⇒ (6). The implication (5) Proof.…”

Section: Direct Sum Decomposability Of Smooth Formsmentioning

confidence: 53%

Direct sum decomposability of polynomials and factorization of associated forms

Fedorchuk

2020

Proc. London Math. Soc.

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We prove two criteria for direct sum decomposability of homogeneous polynomials. For a homogeneous polynomial with a non‐zero discriminant, we interpret direct sum decomposability of the polynomial in terms of factorization properties of the Macaulay inverse system of its Milnor algebra. This leads to an if‐and‐only‐if criterion for direct sum decomposability of such a polynomial, and to an algorithm for computing direct sum decompositions over any field, either of characteristic 0 or of sufficiently large positive characteristic, for which polynomial factorization algorithms exist. For homogeneous forms over algebraically closed fields, we interpret direct sums and their limits as forms that cannot be reconstructed from their Jacobian ideal. We also give simple necessary criteria for direct sum decomposability of arbitrary homogeneous polynomials over arbitrary fields and apply them to prove that many interesting classes of homogeneous polynomials are not direct sums.

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“…For any ω ∈ S ∨ ν with ker ω = I ν , papers [8,9] introduced an associated form of A as the element of D ν given by the formula…”

Section: Associated Forms Of Complete Intersectionsmentioning

confidence: 99%