The Eisenbud-Green-Harris conjecture over fields of characteristic zero

Claims the Eisenbud-Green-Harris conjecture over every field of characteristic zero, for homogeneous regular sequences of any positive length with all degrees at least two and with no growth condition on the degrees, via commuting division-coefficient linear forms whose ordered monomials form a basis of the whole polynomial algebra. It does NOT treat positive characteristic. The Betti-number strengthening (lex-plus-powers) is the companion's result, listed separately.

Claims the Eisenbud-Green-Harris conjecture over every field of characteristic zero, for homogeneous regular sequences of any positive length with all degrees at least two and with no growth condition on the degrees, via commuting division-coefficient linear forms whose ordered monomials form a basis of the whole polynomial algebra. It does NOT treat positive characteristic. The Betti-number strengthening (lex-plus-powers) is the companion's result, listed separately.