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math.AC2026
Bounds for Regularity of Toric Varieties in Terms of Multiplicity
Giulio Caviglia, Kieran Hilmer
The Eisenbud-Goto conjecture stated that for a homogeneous prime ideal in a polynomial ring over an algebraically closed field, the Castelnuovo-Mumford regularity is bounded above…
math.AC2026
Quadratic linear strands of prime ideals
Giulio Caviglia, Alessandro De Stefani
We prove sharp estimates on the quadratic strand of the resolution of any homogeneous prime ideal in a standard graded polynomial ring over an arbitrary field. Our bounds only depe…