Lefschetz properties in algebra, geometry and combinatorics. Abstracts from the workshop held September 27 -- October 3, 2020 (hybrid meeting)

DOI10.4171/OWR/2020/31zbMath1473.00047MaRDI QIDQ2232314

No author found.

Publication date: 5 October 2021

Published in: Oberwolfach Reports (Search for Journal in Brave)

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Proceedings of conferences of miscellaneous specific interest (00B25) Proceedings, conferences, collections, etc. pertaining to combinatorics (05-06) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Combinatorics of partially ordered sets (06A07) Group actions on varieties or schemes (quotients) (14L30) Grassmannians, Schubert varieties, flag manifolds (14M15) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Collections of abstracts of lectures (00B05) Complete intersections (14M10) Actions of groups on commutative rings; invariant theory (13A50) Graded rings (13A02) Syzygies, resolutions, complexes and commutative rings (13D02) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Algebraic aspects of posets (06A11) Proceedings, conferences, collections, etc. pertaining to commutative algebra (13-06) Combinatorial aspects of simplicial complexes (05E45) Combinatorial aspects of commutative algebra (05E40)

Uses Software

• Macaulay2

Cites Work

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• FI-modules over Noetherian rings.
• Resurgences for ideals of special point configurations in \(\mathbb P^N\) coming from hyperplane arrangements
• Sperner property and finite-dimensional Gorenstein algebras associated to matroids
• Hard Lefschetz theorem for simple polytopes
• Finite Gröbner bases in infinite dimensional polynomial rings and applications
• The central simple modules of Artinian Gorenstein algebras
• On Giambelli's theorem on complete correlations
• Syzygy bundles on \(\mathbb P^2\) and the weak Lefschetz property
• Sagbi bases of Cox-Nagata rings
• Separating invariants and finite reflection groups
• Vector bundles on complex projective spaces
• Some remarks on Cohen-Macaulay rings with many zero divisors and an application
• Hilbert functions of graded algebras
• On simple polytopes
• Togliatti systems and Galois coverings
• Hodge theory for combinatorial geometries
• Free and nearly free curves vs. rational cuspidal plane curves
• Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• Unexpected hypersurfaces and where to find them
• On mixed Hessians and the Lefschetz properties
• Finite collineation groups and birational rigidity
• On the arithmetic Cohen-Macaulayness of varieties parameterized by Togliatti systems
• Expecting the unexpected: quantifying the persistence of unexpected hypersurfaces
• The canonical module of GT-varieties and the normal bundle of RL-varieties
• When is a Specht ideal Cohen-Macaulay?
• Togliatti systems associated to the dihedral group and the weak Lefschetz property
• Complete intersection Jordan types in height two
• Betti numbers of symmetric shifted ideals
• Strict log-concavity of the Kirchhoff polynomial and its applications
• Symmetric decomposition of the associated graded algebra of an Artinian Gorenstein algebra
• Vanishing Hessian, wild forms and their border VSP
• On the weak Lefschetz property for vector bundles on \(\mathbb{P}^2\)
• Equivariant coinvariant rings, Bott-Samelson rings and Watanabe's bold conjecture
• On 3-syzygy and unexpected plane curves
• On the weak Lefschetz property for artinian Gorenstein algebras of codimension three
• The minimal free graded resolution of a star-configuration in \(\mathbb{P}^n\)
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• On the weak Lefschetz property for almost complete intersections generated by uniform powers of general linear forms
• The weak Lefschetz property for Artinian Gorenstein algebras of codimension three
• FI- and OI-modules with varying coefficients
• Minimal set of binomial generators for certain Veronese 3-fold projections
• The Jordan type of graded Artinian Gorenstein algebras
• Representations of rational Cherednik algebras with minimal support and torus knots.
• FI-modules and stability for representations of symmetric groups
• The structure of the inverse system of Gorenstein \(k\)-algebras
• Equivariant Hilbert series in non-Noetherian polynomial rings
• Families of Artinian and one-dimensional algebras
• The Lefschetz properties
• Negative curves on algebraic surfaces
• The finite free extension of Artinian \(K\)-algebras with the strong Lefschetz property
• Harbourne, Schenck and Seceleanu's conjecture
• Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
• GL-equivariant modules over polynomial rings in infinitely many variables
• Gröbner methods for representations of combinatorial categories
• Stanley’s nonunimodal Gorenstein $h$-vector is optimal
• Line arrangements and configurations of points with an unexpected geometric property
• Bounded Negativity and Arrangements of Lines
• Noetherianity up to Symmetry
• On the degree two entry of a Gorenstein $h$-vector and a conjecture of Stanley
• The weak Lefschetz property and powers of linear forms in 𝕂[𝕩,𝕪,𝕫]
• Finite generation of symmetric ideals
• An inequality for Hilbert series of graded algebras.
• A nonunimodal graded gorenstein artin algebra in codimension five
• A note on complete intersections of height three
• Gorenstein Artin Algebras and Points in Projective Space
• Associated graded algebra of a Gorenstein Artin algebra
• Torification and factorization of birational maps
• On Cohen–Macaulayness ofS_n-Invariant Subspace Arrangements
• Splitting types of bundles of logarithmic vector fields along plane curves
• The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals
• An analogue of the Hodge-Riemann relations for simple convex polytopes
• Laplace Equations and the Weak Lefschetz Property
• Nearly free curves and arrangements: a vector bundle point of view
• On the Theory of Gordan-Noether on Homogeneous Forms with Zero Hessian (Improved Version)
• Negative Curves on Symmetric Blowups of the Projective Plane, Resurgences, and Waldschmidt Constants
• Castelnuovo–Mumford Regularity up to Symmetry
• Unexpected curves and Togliatti‐type surfaces
• Codimension and projective dimension up to symmetry
• Vandermonde determinantal ideals
• Interpolation and the weak Lefschetz property
• Singular hypersurfaces characterizing the Lefschetz properties
• Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci
• Decomposition of Birational Toric Maps in Blow-Ups and Blow-Downs
• Stanley’s theorem on codimension 3 Gorenstein ℎ-vectors
• Finite Unitary Reflection Groups
• The quadratic complete intersections associated with the action of the symmetric group
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