Algebraic Geometry, Commutative Algebra and Combinatorics: Interactions and Open Problems

B. Harbourne ()
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B. Harbourne: University of Nebraska, Department of Mathematics

A chapter in Commutative Algebra, 2021, pp 445-473 from Springer

Abstract: Abstract We survey recent research bridging algebraic geometry, commutative algebra and combinatorics, highlighting open questions, problems and conjectures of current interest. For expositional simplicity and focus, the emphasis is on homogeneous ideals of fat point subschemes of projective space. The survey is structured into three parts, each part starting with a question, conjecture or result of David Eisenbud. The first part is on the computability of semi-effectivity, the second part is on the containment problem of symbolic powers of ideals of fat points in their ordinary powers, and the third part is on splitting types of rank 2 bundles on rational curves.

Keywords: Ascenzi curves; Asymptotic resurgence; Bounded negativity; Containment problem; Fat points; H-constants; Ideals; Integral Closure; Line arrangements; Modular points; Polynomial interpolation; Polynomial ring; Resurgence; Semi-effectivity; SHGH Conjecture; Splitting type; Supersolvable line arrangements; Symbolic power; Unexpected curves; Waldschmidt constants; Primary: 14H50, 14J26, 13F20, 14N20; Secondary: 13B22, 13D02, 52C30 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-89694-2_14

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DOI: 10.1007/978-3-030-89694-2_14

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