论文标题
关于通过归一化体积的奇异点的界限
On the boundedness of singularities via normalized volume
论文作者
论文摘要
在本文中，我们研究了有关奇点的归一化体积和界限的猜想。我们专注于具有复杂性1，三重奇异性和超表面奇异性的奇异性。考虑到实际值v> 0，我们证明了具有归一化体积至少V的k相吻合的三重奇异性的类别。在N维复杂度-1和n维超表面奇异性的情况下，类似的陈述被证明是arbitary n的。在KLT奇异性的一般情况下，即没有关于K-符号性的假设，我们表明，为了特殊的退化，归一化体积的界限与复杂性-1圆环作用的奇异性界限。我们展示了一个三维示例，该示例表明最后一个语句是最佳的。
In this article we study conjectures regarding normalized volume and boundedness of singularities. We focus on singularities with a torus action of complexity 1, threefold singularities, and hypersurface singularities. Given a real value v>0, we prove that the class of K-semistable threefold singularities with normalized volume at least v forms a bounded family. Analogous statements are proved in the case of n-dimensional complexity-1 and n-dimensional hypersurface singularities for arbitary n. In the general case of klt singularities, i.e. without the assumption on K-semistability, we show that, up to special degenerations, the normalized volume bounds singularities with a complexity-1 torus action. We exhibit a 3-dimensional example which shows that this last statement is optimal.
