2012/08/10 by Giulio Caviglia, Enrico Sbarra, Caviglia, Giulio +1 · 1 citation
Mathematics · #13d02 13d45 14b15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG #msc:13d02 #msc:13d45 #msc:14b15
paper · pdf · doi:10.48550/arxiv.1208.2187
15 pages, 1 figure
openalex publication_date 2012/08/10 · arxiv created 2013/03/11 · arxiv updated 2013/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an inequality between Hilbert functions of local cohomology modules supported in the homogeneous maximal ideal of standard graded algebras over a field, within the framework of embeddings of posets of Hilbert functions. As a main application, we prove an analogue for local cohomology of Evans' Lex-Plus-Power Conjecture for Betti numbers. This results implies some cases of the classical Lex-Plus-Power Conjecture, namely an inequality between extremal Betti numbers. In particular, for the classes of ideals for which the Eisenbud-Green-Harris Conjecture is currently known, the projective dimension and the Castelnuovo-Mumford regularity of a graded ideal do not decrease by passing to the corresponding Lex-Plus-Power ideal.