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Vojta's conjecture on weighted projective varieties

Sajad Salami, Tanush Shaska

I-AIMS paper 2023-01 · Published in Eur. J. Math. 11 (2025), Paper 12 · 2025

We formulate Vojta’s conjecture for smooth weighted projective varieties, weighted multiplier ideal sheaves, and weighted log pairs and prove that all three versions of the conjecture are equivalent. In the process, we introduce generalized weighted general common divisors and express them as heights of weighted projective spaces blown-up relative to an exceptional divisor. Furthermore, we prove that assuming Vojta’s conjecture for weighted projective varieties one can bound the log hwgcd for any subvariety of codimension ≥ 2 and a finite set of places S. An analogue result is proved for weighted homogeneous polynomials with integer coefficients.

MSC classes: Primary 11G50; Secondary 14G40

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