In this note, using methods introduced by Hacon et 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 coefficients Λ satisfies 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 of ε-log canonical varieties, for 0 < ε < 1. In this situation, we prove that if Λ is finite, then the corresponding set of volumes is discrete.

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关于原木品种成交量的几点说明

在本笔记中，使用 Hacon 介绍的方法等人. ['原木一般类型的有界性', Proceedings of Symposia in Pure Mathematics, Volume 97 (American Mathematical Society, Providence, RI, 2018) 309-348]，我们研究了对数一般类型品种的卷的累积点。首先，我们证明如果边界系数集Λ满足降链条件 (DCC)，在限制下关闭并包含 1，则相应的体积集满足 DCC 并在限制下关闭。然后，我们考虑以下情况ε-log 规范变体，对于 0 < ε < 1。在这种情况下，我们证明如果Λ是有限的，则相应的体积集是离散的。