Family 200AlgebraNo LeanNot yet digested
Eisenbud–Green–Harris and lex-plus-powers
Proves the Eisenbud–Green–Harris and lex-plus-powers conjectures over every characteristic-zero field. Any homogeneous ideal containing a regular sequence, of arbitrary length and degrees at least two, admits a lex-plus-powers ideal with the same Hilbert function and no smaller graded Betti numbers.
Manuscripts in this family · 2
The Artinian Lex-Plus-Powers Betti Theorem
Sep 23, 2026·paper.pdf
We prove the Eisenbud–Green–Harris and lex-plus-powers conjectures over every characteristic-zero field for homogeneous regular sequences of any positive length, with degrees at least two. For every homogeneous ideal containing such a sequence, the corresponding lex-plus-powers ideal has the same Hilbert function and at least as large a graded Betti number in every homological and internal degree.
Commuting Division-Coefficient Forms and the Artinian Eisenbud--Green--Harris Conjecture
Sep 23, 2026·paper.pdf
We prove the Eisenbud–Green–Harris conjecture over every characteristic-zero field for homogeneous regular sequences of any positive length, with degrees at least two. Thus every homogeneous ideal containing such a sequence has the Hilbert function of a monomial ideal containing the corresponding pure powers.