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arXiv · 1907.09324

Greatest common divisors of integral points of numerically equivalent divisors

Julie Tzu-Yueh Wang·Yu Yasufuku
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Abstract

We generalize the G.C.D. results of Corvaja--Zannier and Levin on $\mathbb G_m^n$ to more general settings. More specifically, we analyze the height of a closed subscheme of codimension at least $2$ inside an $n$-dimensional Cohen-Macaulay projective variety, and show that this height is small when evaluated at integral points with respect to a divisor $D$ when $D$ is a sum of $n+1$ effective divisors which are all numerically equivalent to some multiples of a fixed ample divisor. Our method is inspired by Silverman's G.C.D. estimate as an application of Vojta's conjecture, which is substituted by a more general version of Schmidt's subspace theorem of Ru--Vojta in our proof.

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BibTeXRIS

Julie Tzu-Yueh Wang, Yu Yasufuku. 2019-07-22. Greatest common divisors of integral points of numerically equivalent divisors. https://doi.org/10.2140/ant.2021.15.287

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