Given a homogeneous ideal I⊆k[x0,…,xn], the Containment problem studies the relation between symbolic and regular powers of I, that is, it asks for which pairs m,r∈N, I(m)⊆Ir holds. In the last years, several conjectures have been posed on this problem, creating an active area of current interests and ongoing investigations. In this paper, we investigated the Stable Harbourne Conjecture and the Stable Harbourne–Huneke Conjecture, and we show that they hold for the defining ideal of a Complement of a Steiner configuration of points in Pnk. We can also show that the ideal of a Complement of a Steiner Configuration of points has expected resurgence, that is, its resurgence is strictly less than its big height, and it also satisfies Chudnovsky and Demailly’s Conjectures. Moreover, given a hypergraph H, we also study the relation between its colourability and the failure of the containment problem for the cover ideal associated to H. We apply these results in the case that H is a Steiner System. View Full-Text

Steiner configurations ideals: Containment and colouring / Ballico, Edoardo; Favacchio, Giuseppe; Guardo, Elena; Milazzo, Lorenzo; Thomas, Abu Chackalamannil. - In: MATHEMATICS. - ISSN 2227-7390. - ELETTRONICO. - 9:3(2021), pp. 210.1-210.15. [10.3390/math9030210]

Steiner configurations ideals: Containment and colouring

Ballico, Edoardo;
2021

Abstract

Given a homogeneous ideal I⊆k[x0,…,xn], the Containment problem studies the relation between symbolic and regular powers of I, that is, it asks for which pairs m,r∈N, I(m)⊆Ir holds. In the last years, several conjectures have been posed on this problem, creating an active area of current interests and ongoing investigations. In this paper, we investigated the Stable Harbourne Conjecture and the Stable Harbourne–Huneke Conjecture, and we show that they hold for the defining ideal of a Complement of a Steiner configuration of points in Pnk. We can also show that the ideal of a Complement of a Steiner Configuration of points has expected resurgence, that is, its resurgence is strictly less than its big height, and it also satisfies Chudnovsky and Demailly’s Conjectures. Moreover, given a hypergraph H, we also study the relation between its colourability and the failure of the containment problem for the cover ideal associated to H. We apply these results in the case that H is a Steiner System. View Full-Text
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Ballico, Edoardo; Favacchio, Giuseppe; Guardo, Elena; Milazzo, Lorenzo; Thomas, Abu Chackalamannil
Steiner configurations ideals: Containment and colouring / Ballico, Edoardo; Favacchio, Giuseppe; Guardo, Elena; Milazzo, Lorenzo; Thomas, Abu Chackalamannil. - In: MATHEMATICS. - ISSN 2227-7390. - ELETTRONICO. - 9:3(2021), pp. 210.1-210.15. [10.3390/math9030210]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/294326
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