The minimal model program for b-log canonical divisors and applications
The minimal model program for b-log canonical divisors and applications
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DOI：
10.1007/s00209-023-03205-w
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发表时间：
2017-07
影响因子：
0.8
通讯作者：
D. Chan;K. Chan;Louis de Thanhoffer de Völcsey-Louis-de-Thanhoffer-de-Völcsey-2210870146;C. Ingalls;K. Jabbusch;S'andor J. Kov'acs;Rajesh S. Kulkarni;Boris Lerner;Basil Nanayakkara;Shinnosuke Okawa;Michel van den Bergh
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作者：
D. Chan;K. Chan;Louis de Thanhoffer de Völcsey-Louis-de-Thanhoffer-de-Völcsey-2210870146;C. Ingalls;K. Jabbusch;S'andor J. Kov'acs;Rajesh S. Kulkarni;Boris Lerner;Basil Nanayakkara;Shinnosuke Okawa;Michel van den Bergh
我们讨论了 forb-log 品种的最小模型程序，它是 a 和 ab-除数的对，作为普通原木品种最小模型程序的自然推广。我们证明了对数 MMP 的主要定理在 b-log MMP 的设置下有效。如果我们假设 log MMP 终止，那么 b-log MMP 也会终止。此外，theb-log MMP 包括 log MMP 和等变 MMP 作为特例。不同的对象产生了各种有趣的博客变体，包括布劳尔对，或“在其中心上有限的非交换代数变体”。更详细地讨论了复曲面布劳尔对的情况。
We discuss the minimal model program forb-log varieties, which is a pair of a variety and ab-divisor, as a natural generalization of the minimal model program for ordinary log varieties. We show that the main theorems of the log MMP work in the setting of theb-log MMP. If we assume that the log MMP terminates, then so does theb-log MMP. Furthermore, theb-log MMP includes both the log MMP and the equivariant MMP as special cases. There are various interestingb-log varieties arising from different objects, including theBrauer pairs, or “non-commutative algebraic varieties which are finite over their centres.” The case of toric Brauer pairs is discussed in further detail.