基于准素的K3曲面
K3 surfaces via almost-primes
摘要：
基于Mukai和Orlov关于K3曲面上的导出范畴的结果和Iwaniec关于几乎-素数的结果，我们注意到以下事实：对于任何给定的正整数N，有N（相互非同构的）射影复K3曲面，使得它们的Picard格不是同构的，但是它们的超越格是Hodge等距的，或者等价地，它们的导出范畴是相互等价的。在回顾了一些有限性结果之后，我们还给出了具有与Picard数为1的X的同构类等价的导出范畴的射影K3曲面的同构类的基数的一个显式公式.
英文摘要：
Based on the result on derived categories on K3 surfaces due to Mukai and Orlov and the result concerning almost-prime numbers due to Iwaniec, we remark the following fact: For any given positive integer N, there are N (mutually non-isomorphic) projective complex K3 surfaces such that their Picard lattices are not isomorphic but their transcendental lattices are Hodge isometric, or equivalently, their derived categories are mutually equivalent. After reviewing some finiteness result, we also give an explicit formula for the cardinality of the isomorphism classes of projective K3 surfaces having derived categories equivalent to the one of X with Picard number 1 in terms of the degree of X.
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