A simple formula for the Picard number of K3 surfaces of BHK type
Christopher Lyons, Bora Olcken
Source record
Source: Crossref
Published: Sep 1, 2020
DOI: 10.1215/21562261-2019-0051
Open original source ↗Source abstract
The Berglund–Hübsch–Krawitz (BHK) mirror symmetry construction applies to certain types of Calabi–Yau varieties that are birational to finite quotients of Fermat varieties. Their definition involves a matrix A and a certain finite abelian group G , and we denote the corresponding Calabi–Yau variety by Z A , G . The transpose matrix A T and the so-called dual group G T give rise to the BHK mirror variety Z A T , G T . In the case of dimension 2, the surface Z A , G is a K3 surface of BHK type. Let Z A , G be a K3 surface of BHK type, with BHK mirror Z A T , G T . Using work of Shioda, Kelly has shown that the geometric Picard number ρ ( Z A , G ) of Z A , G may be expressed in terms of a certain subset of the dual group G T . We simplify this formula significantly to show that ρ ( Z A , G ) depends only upon the degree of the mirror polynomial F A T .
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.