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

In: Commutative Algebra

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  • B. Harbourne

    (University of Nebraska, Department of Mathematics)

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.

Suggested Citation

  • B. Harbourne, 2021. "Algebraic Geometry, Commutative Algebra and Combinatorics: Interactions and Open Problems," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, pages 445-473, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-89694-2_14
    DOI: 10.1007/978-3-030-89694-2_14
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