The alpha problem \& line count configurations

DOI10.1016/j.jalgebra.2014.03.009zbMath1297.13018arXiv1312.4147OpenAlexW2033685428MaRDI QIDQ402674

Stephen G. Hartke, Susan Marie Cooper

Publication date: 28 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4147

zbMATH Keywords

Hilbert functionsFat pointsInitial degrees

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Computational aspects in algebraic geometry (14Q99) Combinatorial aspects of commutative algebra (05E40) Cycles and subschemes (14C99)

Related Items (4)

The symbolic generic initial system of almost linear point configurations in \(\mathbb P^2\) ⋮ Algebraic Geometry, Commutative Algebra and Combinatorics: Interactions and Open Problems ⋮ The Waldschmidt constant of special \(\Bbbk\)-configurations in \(\mathbb{P}^n\) ⋮ Containment results for ideals of various configurations of points in \(\mathbb P^N\)

Cites Work

• Unnamed Item
• Containment results for ideals of various configurations of points in \(\mathbb P^N\)
• Containment counterexamples for ideals of various configurations of points in \(\mathbb{P}^N\)
• Combinatorial bounds on Hilbert functions of fat points in projective space
• The effect of points fattening on postulation
• Generalized test ideals and symbolic powers
• Classifying Hilbert functions of fat point subschemes in \(\mathbb{P}^2\)
• Comparison of symbolic and ordinary powers of ideals.
• Are symbolic powers highly evolved?
• The Hilbert Function of a Reduced K -Algebra
• The resurgence of ideals of points and the containment problem
• Comparing powers and symbolic powers of ideals
• A primer on Seshadri constants
• Evolutions, Symbolic Squares, and Fitting Ideals
• Uniform bounds and symbolic powers on smooth varieties

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