The $$F$$ F -pure threshold of a Calabi–Yau hypersurface

Bhatt, Bhargav; Singh, Anurag K.

doi:10.1007/s00208-014-1129-0

Cited by 17 publications

(46 citation statements)

References 22 publications

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“…We conclude this section by extending Bhatt and Singh's result[2,3.5] using a generalization of their method with an application of the determinant trick used in the proof of [4, 2.1].Theorem 3.5. Using the notation from (3.2), let Jac(R) be the ideal of (c × c) minors of the Jacobianmatrix (∂f j /∂x i ), 0 ≤ i ≤ n, 1 ≤ j ≤ c. Suppose Jac(R) + J = m. If p ≥ (n + 1 − c)(d − c)then the below Frobenius action is injective:F : H n+1−c m (R) <0 → H n+1−c m (R) <0 .Proof.…”

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confidence: 78%

A note on injectivity of Frobenius on local cohomology of global complete intersections

Canton

2016

Journal of Pure and Applied Algebra

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Abstract. Given a graded complete intersection ideal J = (f 1 , . . . , fc) ⊆ k[x 0 , . . . , xn] = S, where k is a field of characteristic p > 0 such that [k : k p ] < ∞, we show that if S/J has an isolated non-F-pure point then the Frobenius action on top local cohomology H n+1−c m (S/J) is injective in sufficiently negative degrees, and we compute the least degree of any kernel element. If S/J has an isolated singularity, we are also able to give an effective bound on p ensuring the Frobenius action on H n+1−c m (S/J) is injective in all negative degrees, extending a result of Bhatt and Singh in the hypersurface case.

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confidence: 78%

A note on injectivity of Frobenius on local cohomology of global complete intersections

Canton

2016

Journal of Pure and Applied Algebra

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“…Recent studies ( [TW04], [Tak13], [HnBWZ16]) reveal that F -pure thresholds have a strong connection to log canonical thresholds in characteristic 0. Moreover, as seen in [TW04], [MTW05] and [BS15], the F -pure threshold itself is an interesting invariant in both commutative algebra and algebraic geometry in positive characteristic.…”

Section: Introductionmentioning

confidence: 99%

Ascending Chain Condition for F-Pure Thresholds with Fixed Embedding Dimension

Sato

2019

International Mathematics Research Notices

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In this paper, we prove that the set of all F -pure thresholds of ideals with fixed embedding dimension satisfies the ascending chain condition. As a corollary, given an integer d, we verify the ascending chain condition for the set of all F -pure thresholds on all d-dimensional normal l.c.i. varieties. In the process of proving these results, we also show the rationality of F -pure thresholds of ideals on non-strongly F -regular pairs.

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“…Bhatt and Singh provide a couple of proofs in [2] using a translation into local cohomology; Generalizations can be found in [14]. In contrast, our approach involves directly investigating the form of f raised to integer powers using a generalized formula of the well known polynomial H p (λ) = n i=0 m i 2 λ i with m = (p − 1)/2, used to compute the Hasse invariant.…”

Section: Introductionmentioning

confidence: 99%