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Miller, Claudia ; Striuli, Janet ; Witt, Emily (Ed.)
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Faber, Eleonore ; Juhnke-Kubitzke, Martina ; Lindo, Haydee ; Miller, Claudia ; R. G., Rebecca ; Seceleanu, Alexandra ( , Association for Women in Mathematics series)Miller, Claudia ; Striuli, Janet ; Witt, Emily (Ed.)We generalize Buchsbaum and Eisenbud’s resolutions for the powers of the maximal ideal of a polynomial ring to resolve powers of the homogeneous maximal ideal over graded Koszul algebras.more » « less
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Kadyrsizova, Zhibek ; Kenkel, Jennifer ; Page, Janet ; Singh, Jyoti ; Smith, Karen E. ; Vraciu, Adela ; Witt, Emily E. ( , Women in Commutative Algebra: Proceedings of the 2019 WICA Workshop)Miller, Claudia ; Striuli, Janet ; Witt, Emily E. (Ed.)Cubic surfaces in characteristic two are investigated from the point of view of prime characteristic commutative algebra. In particular, we prove that the non-Frobenius split cubic surfaces form a linear subspace of codimension four in the 19-dimensional space of all cubics, and that up to projective equivalence, there are finitely many non-Frobenius split cubic surfaces. We explicitly describe defining equations for each and characterize them as extremal in terms of configurations of lines on them. In particular, a (possibly singular) cubic surface in characteristic two fails to be Frobenius split if and only if no three lines on it form a “triangle”.more » « less