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The Weak Lefschetz Property of Equigenerated Monomial Ideals
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
(engelsk)Inngår i: Artikkel i tidsskrift (Annet vitenskapelig) Accepted
Abstract [en]

We determine the sharp lower bound for the Hilbert function in degree d of a

monomial algebra failing the WLP over a polynomial ring with n variables and generated in

degree d. We consider artinian ideals in the polynomial ring with

n variables generated by homogeneous polynomials of degree d invariant under an action of

the cyclic group Z/dZ. We give a complete classification of

such ideals in terms of the WLP depending on the action.

Emneord [en]
The Weak Lefschetz property, Monomial ideal, Group action
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:kth:diva-223381OAI: oai:DiVA.org:kth-223381DiVA, id: diva2:1183902
Merknad

QC 20180220

Tilgjengelig fra: 2018-02-19 Laget: 2018-02-19 Sist oppdatert: 2018-02-20bibliografisk kontrollert
Inngår i avhandling
1. Lefschetz Properties of Monomial Ideals
Åpne denne publikasjonen i ny fane eller vindu >>Lefschetz Properties of Monomial Ideals
2018 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis concerns the study of the Lefschetz properties of artinian monomial algebras. An artinian algebra is said to satisfy the strong Lefschetz property if multiplication by all powers of a general linear form has maximal rank in every degree. If it holds for the first power it is said to have the weak Lefschetz property (WLP).

In the first paper, we study the Lefschetz properties of monomial algebras by studying their minimal free resolutions. In particular, we give an afirmative answer to an specific case of a conjecture by Eisenbud, Huneke and Ulrich for algebras having almost linear resolutions. Since many algebras are expected to have the Lefschetz properties, studying algebras failing the Lefschetz properties is of a great interest. In the second paper, we provide sharp lower bounds for the number of generators of monomial ideals failing the WLP extending a result by Mezzetti and Miró-Roig which provides upper bounds for such ideals. In the second paper, we also study the WLP of ideals generated by forms of a certain degree invariant under an action of a cyclic group. We give a complete classication of such ideals satisfying the WLP in terms of the representation of the group generalizing a result by Mezzetti and Miró-Roig.

sted, utgiver, år, opplag, sider
Kungliga Tekniska högskolan, 2018
Emneord
Weak Lefschetz property, monomial ideals, group actions, almost linear resolution
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
urn:nbn:se:kth:diva-223373 (URN)978-91-7729-703-1 (ISBN)
Presentation
2018-03-16, F11, Lindstedtsvagen 24, KTH, Stockholm, 14:00 (engelsk)
Opponent
Veileder
Merknad

QC 20180220

Tilgjengelig fra: 2018-02-20 Laget: 2018-02-19 Sist oppdatert: 2018-02-20bibliografisk kontrollert

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