Complements on log canonical Fano varieties
Yanning Xu
TL;DR
This paper extends the theory of complements to log canonical log Fano varieties, establishing boundedness results in low dimensions and exploring properties of log Calabi-Yau varieties.
Contribution
It generalizes the theory of complements to a broader class of varieties and proves boundedness in dimensions up to three, with additional results on log Calabi-Yau varieties.
Findings
Boundedness of complements for log canonical log Fano varieties in dimension ≤ 3.
Boundedness results for the canonical index of sdlt log Calabi-Yau varieties in dimension 2.
Extension of complement theory to new classes of algebraic varieties.
Abstract
In this paper, we generalise the theory of complements to log canonical log fano varieties and prove boundedness of complements for them in dimension less than or equal to 3. We also prove some boundedness results for the canonical index of sdlt log Calabi-Yau varieties in dimension 2.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Meromorphic and Entire Functions