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We classify 4-dimensional austere submanifolds in Euclidean space ruled by 2-planes. The algebraic possibilities for second fundamental forms of an austere 4-fold M were classified by Bryant, falling...
On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension Four
Hilbert Functions Gorenstein Artin Algebras
2010/11/18
We prove that the Hilbert functions of codimension four graded Gorenstein Artin algebras R/I are unimodal provided I has a minimal generator in degree less than five. It is an open question whether al...