| 1. |
- Sumaila, U. Rashid, et al.
(författare)
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WTO must ban harmful fisheries subsidies
- 2021
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Ingår i: Science. - : American Association for the Advancement of Science (AAAS). - 0036-8075 .- 1095-9203. ; 374:6567, s. 544-544
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 2. |
- Abdallah, Nancy, et al.
(författare)
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Combinatorial invariance of Kazhdan-Lusztig-Vogan polynomials for fixed point free involutions
- 2018
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Ingår i: Journal of Algebraic Combinatorics. - : SPRINGER. - 0925-9899 .- 1572-9192. ; 47:4, s. 543-560
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Tidskriftsartikel (refereegranskat)abstract
- When acts on the flag variety of , the orbits are in bijection with fixed point free involutions in the symmetric group . In this case, the associated Kazhdan-Lusztig-Vogan polynomials can be indexed by pairs of fixed point free involutions , where denotes the Bruhat order on . We prove that these polynomials are combinatorial invariants in the sense that if is a poset isomorphism of upper intervals in the Bruhat order on fixed point free involutions, then for all v amp;gt;= u.
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| 3. |
- Abdallah, Nancy, et al.
(författare)
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Free resolutions and Lefschetz properties of some Artin Gorenstein rings of codimension four
- 2024
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Ingår i: Journal of symbolic computation. - 0747-7171 .- 1095-855X. ; 121, s. 102257-102257
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Tidskriftsartikel (refereegranskat)abstract
- In (Stanley, 1978), Stanley constructs an example of an Artinian Gorenstein (AG) ring A with non-unimodal H-vector (1,13,12,13,1). Migliore-Zanello show in (Migliore and Zanello, 2017) that for regularity r=4, Stanley's example has the smallest possible codimension c for an AG ring with non-unimodal H-vector.The weak Lefschetz property (WLP) has been much studied for AG rings; it is easy to show that an AG ring with non-unimodal H-vector fails to have WLP. In codimension c=3 it is conjectured that all AG rings have WLP. For c=4, Gondim shows in (Gondim, 2017) that WLP always holds for r≤4 and gives a family where WLP fails for any r≥7, building on Ikeda's example (Ikeda, 1996) of failure for r=5. In this note we study the minimal free resolution of A and relation to Lefschetz properties (both weak and strong) and Jordan type for c=4 and r≤6.
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| 4. |
- Abdallah, Nancy, et al.
(författare)
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Lefschetz properties of some codimension three Artinian Gorenstein algebras
- 2023
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 625, s. 28-45
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Tidskriftsartikel (refereegranskat)abstract
- Codimension two Artinian algebras have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three Artinian Gorenstein algebras. Despite much work, the strong Lefschetz property for codimension three Artinian Gorenstein algebra has remained largely mysterious; our results build on and strengthen some of the previous results. We here show that every standard-graded codimension three Artinian Gorenstein algebra A having maximum value of the Hilbert function at most six has the strong Lefschetz property, provided that the characteristic is zero. When the characteristic is greater than the socle degree of A, we show that A is almost strong Lefschetz, they are strong Lefschetz except in the extremal pair of degrees.
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| 5. |
- Abdallah, Nancy, et al.
(författare)
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Limits of graded Gorenstein algebras of Hilbert function $$(1,3^k,1)$$
- 2024
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Ingår i: European Journal of Mathematics. - 2199-675X .- 2199-6768. ; 10:1
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Tidskriftsartikel (refereegranskat)abstract
- Let R= k [x, y, z], the polynomial ring over a field k. Several of the authors previously classified nets of ternary conics and their specializations over an algebraically closed field, Abdallah et al. (Eur J Math 9(2), Art. No. 22, 2023). We here show that when k is algebraically closed, and considering the Hilbert function sequence T =(1,3(k),1), k >= 2 (i.e. T = (1, 3, 3, ... , 3, 1) where k is the multiplicity of 3), then the family GT parametrizing graded Artinian algebra quotients A = R/I of R having Hilbert function T is irreducible, and G(T) is the closure of the family Gor(T) of Artinian Gorenstein algebras of Hilbert function T. We then classify up to isomorphism the elements of these families Gor(T) and of G(T). Finally, we give examples of codimension 3 Gorenstein sequences, such as (1, 3, 5, 3, 1), for which G(T) has several irreducible components, one being the Zariski closure of Gor(T).
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| 6. |
- Abdallah, Nancy, et al.
(författare)
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Nets in P^2 and Alexander Duality
- 2023
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Ingår i: Discrete & Computational Geometry. - 0179-5376 .- 1432-0444.
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Tidskriftsartikel (refereegranskat)abstract
- A net in P^2 is a configuration of lines A and points X satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac–Moody algebras to cohomology jump loci of hyperplane arrangements. For a matroid M and rank r, we associate a monomial ideal (a monomial variant of the Orlik–Solomon ideal) to the set of flats of M of rank ≤r. In the context of line arrangements in P^2, applying Alexander duality to the resulting ideal yields insight into the combinatorial structure of nets.
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| 7. |
- Abdallah, Nancy, et al.
(författare)
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Nets of conics and associated Artinian algebras of length 7
- 2023
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Ingår i: European Journal of Mathematics. - : Springer Science and Business Media LLC. - 2199-675X .- 2199-6768. ; 9:2
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Tidskriftsartikel (refereegranskat)abstract
- We classify the orbits of nets of conics under the action of the projective linear group and we determine the specializations of these orbits, using geometric and algebraic methods. We study related geometric questions, as the parametrization of planar cubics. We show that Artinian algebras of Hilbert function H=(1,3,3,0) determined by nets, can be smoothed—deformed to a direct sum of fields; and that algebras of Hilbert function H=(1,r,2,0), determined by pencils of quadrics, can also be smoothed. This portion is a translation and update of a 1977 version, a typescript by the second two authors that was distributed as a preprint of University of Paris VII. In a new Historical Appendix A we describe related work prior to 1977. In an Update Appendix B we survey some developments since 1977 concerning nets of conics, related geometry, and deformations of Artinian algebras of small length.
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| 8. |
- Abdallah, Nancy
(författare)
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On Hodge Theory of Singular Plane Curves
- 2016
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Ingår i: Canadian mathematical bulletin. - : Canadian Mathematical Society. - 0008-4395 .- 1496-4287. ; 59:3, s. 449-460
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Tidskriftsartikel (refereegranskat)abstract
- The dimensions of the graded quotients of the cohomology of a plane curve complement U = P-2/C with respect to the Hodge filtration are described in terms of simple geometrical invariants. The case of curves with ordinary singularities is discussed in detail. We also give a precise numerical estimate for the difference between the Hodge filtration and the pole order filtration on H-2(U, C).
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| 9. |
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| 10. |
- Abdallah, Nancy, et al.
(författare)
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Topology of posets with special partial matchings
- 2019
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Ingår i: Advances in Mathematics. - : Academic Press. - 0001-8708 .- 1090-2082. ; 348, s. 255-276
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Tidskriftsartikel (refereegranskat)abstract
- Special partial matchings (SPMs) are a generalisation of Brentis special matchings. Let a pircon be a poset in which every non-trivial principal order ideal is finite and admits an SPM. Thus pircons generalise Mariettis zircons. We prove that every open interval in a pircon is a PL ball or a PL sphere. It is then demonstrated that Bruhat orders on certain twisted identities and quasiparabolic W-sets constitute pircons. Together, these results extend a result of Can, Cherniaysky, and Twelbeck, prove a conjecture of Hultman, and confirm a claim of Rains and Vazirani.
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