K3 surfaces with algebraic period ratios have complex multiplication Conference Paper

abstract

• Let be a non-zero holomorphic 2-form on a K3 surface S. Suppose that S is projective algebraic and is defined over [Formula: see text]. Let [Formula: see text] be the [Formula: see text]-vector space generated by the numbers given by all the periods , H2(S, ). We show that, if [Formula: see text], then S has complex multiplication, meaning that the MumfordTate group of the rational Hodge structure on H2(S, ) is abelian. This result was announced in [P. Tretkoff, Transcendence and CM on BorceaVoisin towers of CalabiYau manifolds, J. Number Theory152 (2015) 118155], without a detailed proof. The converse is already well known.

authors

• Tretkoff, Paula

published proceedings

• INTERNATIONAL JOURNAL OF NUMBER THEORY

author list (cited authors)

• Tretkoff, P.

citation count

• 3

complete list of authors

• Tretkoff, Paula

publication date

• August 2015

publisher

• World Scientific Publishing  Publisher

published in

• International Journal of Number Theory  Journal

keywords

• Complex Multiplication
• K3 Surfaces
• Periods
• Transcendence

Digital Object Identifier (DOI)

• 10.1142/S1793042115400217

start page

• 1709

end page

• 1724

volume

• 11

issue

• 5

URL

• http%3A%2F%2Fdx.doi.org%2F10.1142%2Fs1793042115400217