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Elliptic Genera of singular varieties, orbifold elliptic genus and chiral deRham complex
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This paper surveys the authors recent work on two variable elliptic genus of singular varieties. The last section calculates a generating function for the elliptic genera of symmetric products. This generalizes the classical results of Macdonald and Zagier.
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The dimension threshold for Batyrev's non-negativity conjecture on stringy Hodge numbers
Batyrev's non-negativity conjecture on stringy Hodge numbers is true for Gorenstein canonical projective varieties in dimension at most 4 and false in all dimensions 5 and higher.
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