On complete intersections with trivial canonical class
Lev A. Borisov, Zhan Li
TL;DR
This paper establishes boundedness results for complete intersections with trivial canonical class in Fano varieties, showing that the set of Hodge numbers produced by Batyrev-Borisov toric constructions is finite in each dimension.
Contribution
It proves birational boundedness for certain complete intersections and demonstrates boundedness of Hodge numbers from toric constructions across dimensions.
Findings
Boundedness of complete intersections with trivial canonical class.
Finiteness of Hodge numbers from Batyrev-Borisov toric constructions.
Applicability to various dimensions and codimensions.
Abstract
We prove birational boundedness results on complete intersections with trivial canonical class of base point free divisors in (some version of) Fano varieties. Our results imply in particular that Batyrev-Borisov toric construction produces only a bounded set of Hodge numbers in any given dimension, even as the codimension is allowed to grow.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Geometric and Algebraic Topology