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Creators/Authors contains: "Wang, Chengxi"

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  1. ; ; (, Transactions of the American Mathematical Society, Series B)
    We construct smooth projective varieties of general type with the smallest known volume and others with the most known vanishing plurigenera in high dimensions. The optimal volume bound is expected to decay doubly exponentially with dimension, and our examples achieve this decay rate. We also consider the analogous questions for other types of varieties. For example, in every dimension we conjecture the terminal Fano variety of minimal volume, and the canonical Calabi-Yau variety of minimal volume. In each case, our examples exhibit doubly exponential behavior. 
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  2. ; (, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE)
    By Hacon-McKernan-Xu, there is a positive lower bound in each dimension for the volumes of all klt varieties with ample canonical class. We show that these bounds must go to zero extremely fast as the dimension increases, by constructing a klt n-fold with ample canonical class whose volume is less than 1/2^{2^n}. These examples should be close to optimal. We also construct, for every n, a klt Fano variety of dimension n such that the space of sections of the mth power of the anticanonical bundle is zero for all m from 1 to about 2^{2^n}. Here again there is some bound in each dimension, by Birkar’s theorem on boundedness of complements, and we are showing that the bound must increase extremely fast with the dimension. 
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  3. ; ; ; (, Journal of Fourier Analysis and Applications)
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