Boij-Söderberg theory: Introduction and survey

Abstract

Boij-Söderberg theory describes the Betti diagrams of graded modules over the polynomial ring up to multiplication by a rational number. Analog Eisenbud-Schreyer theory also describes the cohomology tables of vector bundles on projective spaces up to rational multiple. We give an introduction and survey of these newly developed areas.

Minor corrections. 47 pages, to appear in Progress in Commutative Algebra: Ring Theory, Homology, and Decomposition, eds. C.Francisco et.al

References in corpus (5)

• Betti Numbers of Graph Ideals
• Tensor complexes: Multilinear free resolutions constructed from higher tensors
• Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case
• Algebraic properties of the path ideal of a tree
• Dependence of Betti Numbers on Characteristic

Cited by in corpus (11)

• Valuations and Frobenius
• On the three dimensional minimal model program in positive characteristic
• Closure operations that induce big Cohen-Macaulay modules and classification of singularities
• Betti numbers of monomial ideals via facet covers
• The gamma construction and asymptotic invariants of line bundles over arbitrary fields
• The Cohomology Annihilator of a Curve Singularity
• On the Lex-plus-powers Conjecture
• Tilting complexes and codimension functions over commutative noetherian rings
• On tame ramification and centers of $F$-purity
• Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains
• How to extend closure and interior operations to more modules