Varieties of general type with doubly exponential asymptotics

Louis Esser, Burt Totaro, Chengxi Wang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)288-309
Number of pages22
JournalTransactions of the American Mathematical Society Series B
StatePublished - 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


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