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Creators/Authors contains: "Kadyrsizova, Zhibek"

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  1. ; ; ; ; ; ; (, Transactions of the American Mathematical Society, Series B)
    We prove that if f f is a reduced homogeneous polynomial of degree d d , then its F F -pure threshold at the unique homogeneous maximal ideal is at least 1 d − 1 \frac {1}{d-1} . We show, furthermore, that its F F -pure threshold equals 1 d − 1 \frac {1}{d-1} if and only if f ∈ m [ q ] f\in \mathfrak m^{[q]} and d = q + 1 d=q+1 , where q q is a power of p p . Up to linear changes of coordinates (over a fixed algebraically closed field), we classify such “extremal singularities”, and show that there is at most one with isolated singularity. Finally, we indicate several ways in which the projective hypersurfaces defined by such forms are “extremal”, for example, in terms of the configurations of lines they can contain. 
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  2. ; ; ; ; ; ; (, Transactions of the American Mathematical Society)
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  3. ; ; ; ; ; ; (, 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”. 
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  4. ; ; ; ; ; ; ; ; ; (, Journal of Software for Algebra and Geometry)
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