LOWER BOUNDS ON THE F-PURE THRESHOLD AND EXTREMAL SINGULARITIES
Kadyrsizova Z. Kenkel J. Page J. Singh J. Smith K.E. Vraciu A. Witt E.E.
2022American Mathematical Society
Transactions of the American Mathematical Society Series B
2022#9Issue 31977 - 1005 pp.
We prove that if f is a reduced homogeneous polynomial of degree d, then its F-pure threshold at the unique homogeneous maximal ideal is at 1 least d−1. We show, furthermore, that itsF-pure threshold equals 1 if and d−1 only if f ∈ m[q] and d = q +1, where q is a power of 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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Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Mathematics, University of Michigan, Ann Arbor, 48109, MI, United States
Department of Mathematics, North Dakota State University, Fargo, 58105, ND, United States
Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, India
Department of Mathematics, University of South Carolina, Columbia, 29208, SC, United States
Department of Mathematics, University of Kansas, Lawrence, 66045, KS, United States
Nazarbayev University
Department of Mathematics
Department of Mathematics
Department of Mathematics
Department of Mathematics
Department of Mathematics
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