Lefschetz properties for complete intersection ideals generated by products of linear forms

Juhnke-Kubitzke, Martina; Miró‐Roig, Rosa M.; Murai, Shinji; Wachi, Akihito

doi:10.1090/proc/14009

Cited by 5 publications

(3 citation statements)

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“…Example 1. In [7] it is proved that a certain class of complete intersections generated by products of linear forms have the SLP. The key to the result is that one can compute initial ideals, and prove that these monomial ideals have the SLP.…”

Section: A Basis Splitting Argument For Monomial Algebrasmentioning

confidence: 99%

“…We also give examples in the literature which can be seen as special cases of our method, and which inspired us to investigate the basis splitting argument; a result on the WLP for powers of monomial complete intersections by Boij, Fröberg and the second author [1], and a result on the SLP of complete intersections of products of linear forms by Juhnke-Kubitzke, Miró-Roig, Murai, and Wachi [7].…”

Section: Introductionmentioning

confidence: 99%

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On decomposing monomial algebras with the Lefschetz properties

Gasanova,

Lundqvist,

Nicklasson

2020

Preprint

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We introduce a general technique for decomposing monomial algebras which we use to study the Lefschetz properties. We apply our technique to various classes of algebras, including monomial almost complete intersections and Gorenstein algebras. In particular, we prove that Gorenstein codimension three algebras arising from numerical semigroups have the strong Lefschetz property. We also study the reverse of the splitting operation -a gluing operation -which gives a way to construct monomial algebras with the Lefschetz properties.

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Section: A Basis Splitting Argument For Monomial Algebrasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On decomposing monomial algebras with the Lefschetz properties

Gasanova,

Lundqvist,

Nicklasson

2020

Preprint

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“…Many other natural algebras lend themselves to questions about the WLP or the SLP. A popular instance is that the underlying ideal is generated by powers of linear forms (see, for instance, [33]). Most of the results achieved in this direction rely on a result of Emsalem and Iarrobino [21], that translates the problem of whether the considered algebra has the WLP to one of studying sets of fat points in a projective space.…”

Section: Introductionmentioning

confidence: 99%

Intersections of Amoebas

Juhnke-Kubitzke

Wolff²

2020

Discrete Mathematics &Amp; Theoretical Computer Science

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International audience Amoebas are projections of complex algebraic varieties in the algebraic torus under a Log-absolute value map, which have connections to various mathematical subjects. While amoebas of hypersurfaces have been inten- sively studied during the last years, the non-hypersurface case is barely understood so far. We investigate intersections of amoebas of n hypersurfaces in (C∗)n, which are genuine supersets of amoebas given by non-hypersurface vari- eties. Our main results are amoeba analogs of Bernstein's Theorem and Be ́zout's Theorem providing an upper bound for the number of connected components of such intersections. Moreover, we show that the order map for hypersur- face amoebas can be generalized in a natural way to intersections of amoebas. We show that, analogous to the case of amoebas of hypersurfaces, the restriction of this generalized order map to a single connected component is still 1-to-1.

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