Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.
Hodge theory for combinatorial geometries
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Combinatorial presentations for algebraic cobordism rings of matroid toric varieties yield an isomorphism to Chow rings tensored with point cobordism, plus isomorphisms for wonderful varieties of hyperplane arrangements.
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Frobenius identities for the volume map on Cohen--Macaulay rings
Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.