Abstract
AbstractIn this note, using methods introduced by Haconet al. [‘Boundedness of varieties of log general type’, Proceedings of Symposia in Pure Mathematics, Volume 97 (American Mathematical Society, Providence, RI, 2018) 309–348], we study the accumulation points of volumes of varieties of log general type. First, we show that if the set of boundary coefficientsΛsatisfies the descending chain condition (DCC), is closed under limits and contains 1, then the corresponding set of volumes satisfies the DCC and is closed under limits. Then, we consider the case ofε-log canonical varieties, for 0 < ε < 1. In this situation, we prove that ifΛis finite, then the corresponding set of volumes is discrete.
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