On structures and discrepancies of klt Calabi--Yau pairs
Junpeng Jiao
TL;DR
This paper investigates the structural properties of klt Calabi--Yau pairs, demonstrating finiteness in discrepancies and bounding the index of certain non-canonical varieties, advancing understanding in algebraic geometry.
Contribution
It establishes the finiteness of discrepancies of log centers and provides bounds on the index of 4-dimensional non-canonical Calabi--Yau varieties.
Findings
Discrepancies of log centers are in a finite set for fixed dimension.
The index of 4-dimensional non-canonical Calabi--Yau varieties is bounded.
Provides structural insights into klt Calabi--Yau pairs.
Abstract
We study the structures of klt Calabi--Yau pairs. We show that the discrepancies of log centers of all klt Calabi--Yau varieties with fixed dimension are in a finite set. As a corollary, we show that the index of 4-dimensional non-canonical Calabi--Yau variety is bounded.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometry and complex manifolds · Algebraic Geometry and Number Theory