Sparsity of Integral Points on Moduli Spaces of Varieties
arxiv(2022)
摘要
Let $X$ be a quasi-projective variety over a number field, admitting (after passage to $\mathbb{C}$) a geometric variation of Hodge structure whose period mapping has zero-dimensional fibers. Then the integral points of $X$ are sparse: the number of such points of height $\leq B$ grows slower than any positive power of $B$. For example, homogeneous integral polynomials in a fixed number of variables and degree, with discriminant divisible only by a fixed set of primes, are sparse when considered up to integral linear substitutions.
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关键词
moduli spaces,sparsity,integral points
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