Titlebook: Lefschetz Properties; Current and New Dire Uwe Nagel,Karim Adiprasito,Satoshi Murai Conference proceedings 2024 The Editor(s) (if applicabl

Barrister

,Totally Nonnegative Toeplitz Matrices and Hodge-Riemann Relations in Codimension Two,is equal to the set of totally nonnegative Toeplitz matrices. The proof appeals to an interpretation of a Toeplitz matrix as the coefficient matrix of the higher mixed Hessian of a homogeneous polynomial in two variables. Regarding the homogeneous polynomial as the Macaulay dual generator of a certa

胆小懦夫

Notes on Lefschetz Properties and Linear Elements of Maximal Height with Applications,lay’s Double Duality Theorem in the guise of inverse systems to provide a criterion for the existance of such a form. We adopt the viewpoint that the presence or lack of a linear form of maximal height is a test for the strong Lefschetz property in a Poincaré duality algebra. In characteristic zero

核心

,List of Problems, a breakthrough in algebraic topology and geometry. Over the last few years, this topic has attracted increasing attention from mathematicians in various areas. Here, we suggest some important open problems about or related to Lefschetz properties of Artinian graded algebras with the ultimate aim to

affluent

迅速飞过

,Totally Nonnegative Toeplitz Matrices and Hodge-Riemann Relations in Codimension Two,his short note is based on results from the longer paper “Higher Lorentzian polynomials, Higher Hessians, and Hodge-Riemann relations on Artinian Gorenstein algebras in codimension two” by P. Macias Marques, C. McDaniel, A. Seceleanu, and J. Watanabe (.).

大酒杯

grandiose

,Unexpected Hypersurfaces and Their Consequences: A Survey,ots of this theory. First we look at sets of points in . whose general projection is a planar complete intersection (so-called . sets). Although we now know a lot about these sets, much remains mysterious. Then we describe an interesting measure of unexpectedness called .-., which have a surprising structure that is not yet fully understood.

charisma

,Equivariant Euler Characteristics on Permutohedral Varieties,uivariant .-theory and thus the Euler characteristic may be upgraded to a Laurent polynomial. We provide and implement three different approaches, in particular a recursive one, to computing these polynomials.

含糊其辞

,Betti Tables Forcing Failure of the Weak Lefschetz Property,gel [.]. Our specific focus is on Betti tables rather than Hilbert functions, and we prove that a certain type of Betti table forces the failure of the Weak Lefschetz Property (WLP). The corresponding Artinian algebras are typically not level, and the failure of WLP in these cases is not detected in terms of the Hilbert function.

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