Over every characteristic-zero field, for a homogeneous ideal containing a regular sequence of any positive length with degrees at least two, a 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.
Over every characteristic-zero field, for a homogeneous ideal containing a regular sequence of any positive length with degrees at least two, a 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.
Over every characteristic-zero field, for a homogeneous ideal containing a regular sequence of any positive length with degrees at least two, a 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.
If correct, resolves the Eisenbud–Green–Harris and lex-plus-powers conjectures in the stated characteristic-zero setting.
Do lex-plus-powers ideals dominate Betti numbers for every characteristic-zero regular sequence?
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OpenAI reports the lex-plus-powers Betti theorem in characteristic zero
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