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Regularity Bounds by Projection

In: Commutative Algebra

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  • Wenbo Niu

    (University of Arkansas, Department of Mathematical Sciences)

Abstract

In this expository paper, we review the method of generic projection that is used to bound the Castelnuovo-Mumford of a projective variety. We extend this method from the classic nonsingular case to the Cohen-Macaulay case. In order to apply this method, one needs to understand the complexity of the fibers of a general projection. In several cases, the method has led to the optimal regularity bound conjectured by Eisenbud-Goto, although the conjecture has been disproved by McCullough-Peeva for singular varieties. We also discuss classical regularity bounds obtained by Castelnuovo and Mumford, and some new results from the recent research.

Suggested Citation

  • Wenbo Niu, 2021. "Regularity Bounds by Projection," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, pages 617-638, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-89694-2_20
    DOI: 10.1007/978-3-030-89694-2_20
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