Syzygies and Hilbert Functions

ISBN-13: 9781138454316 / Angielski / Twarda / 2018 / 304 str.

Irena Peeva

Opis

Examines the invariant of Castelnuovo-Mumford regularity, blowup algebras, and bigraded rings. This work outlines the status of two conjectures: the lex-plus-power (LPP) conjecture and the multiplicity conjecture. It considers minimal free resolutions of integral subschemes and of equidimensional Cohen-Macaulay subschemes of small degree.

Spis treści

Introduction. Some Results and Questions on Castelnuovo-Mumford Regularity. Hilbert Coefficients of Ideals With a View Toward Blowup Algebra. A Case Study in Bigraded Commutative Algebra. Lex-plus-powers Ideals. Multiplicity Conjectures. The Geometry of Hilbert Functions. Resolutions of Subschemes of Small Degree. Koszul Toric Rings. Resolutions and Subspace Arrangements. Multi-graded Hilbert Functions, Mixed Multiplicities.

O autorze

Irena Peeva is a professor of mathematics at Cornell University.