Weak positivity theorem and Frobenius stable canonical rings of geometric generic fibers

Ejiri, Sho

doi:10.1090/jag/698

Cited by 19 publications

(36 citation statements)

References 36 publications

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“…Then the assertion follows from the arguments of [, Section 4, Step 1–4] by replacing

K_{X}

with

K_{X} + B

. In case (iii), combining results of [, Corollary 2.23], we see that all the conditions of [, Theorem 1.4] are satisfied, hence the assertion follows. In case (iv), the assertion is [, Remark 3.3].

□

…”

Section: Preliminariesmentioning

confidence: 67%

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Abundance for non‐uniruled 3‐folds with non‐trivial Albanese maps in positive characteristics

Zhang

2018

J. London Math. Soc.

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“…Then the assertion follows from the arguments of [, Section 4, Step 1–4] by replacing

K_{X}

with

K_{X} + B

. In case (iii), combining results of [, Corollary 2.23], we see that all the conditions of [, Theorem 1.4] are satisfied, hence the assertion follows. In case (iv), the assertion is [, Remark 3.3].

□

…”

Section: Preliminariesmentioning

confidence: 67%

“…We collect some results which will be used in the sequel. For more general results on this topic please refer to [, , , , ]. Theorem Assume

char k = p > 5

.…”

Section: Preliminariesmentioning

confidence: 99%

Abundance for non‐uniruled 3‐folds with non‐trivial Albanese maps in positive characteristics

Zhang

2018

J. London Math. Soc.

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“…The proof combines ideas of [16] and [36]. When the geometric generic fiber X η has strongly F -regular singularities and K X is f -big, similar result has been proved by Ejiri [15] and Zhang [36]. Let's review their approaches.…”

Section: Introductionmentioning

confidence: 74%

“…Up to now, the following have been proved (i) W C n,n−1 and C 2,1 ([10]); (ii) W C 3,1 (overF p , p > 5 by [6], over general k with char k > 5 by [15] and [16]); (iii) C 3,1 under the situation that K Xη is big, g(Y ) > 1 and char k > 5 ( [36]).…”

Section: Introductionmentioning

confidence: 99%