A conjectured analogue of Dedekind's eta function for \(K3\) surfaces
type: Item
instance of: scholarly article
title: A conjectured analogue of Dedekind's eta function for \(K3\) surfaces
zbMATH Open document ID: 0858.14020
published in: Mathematical Research Letters
publication date: 1995-11-16T00:00:00Z
review text: For \(\tau\in \mathbb{C}\) let \(E_\tau =\mathbb{C}/ \Lambda_\tau\) be the associated elliptic curve; the Dedekind's eta function \(\eta (\tau)\) provides a formula for the product of the non 0 eigenvalues of the Laplacian \(\Delta= -4b \partial^2/ \partial z \partial \overline z\). This theory has been extended to K3 surfaces, by means of a function \(f_e\) defined in the space of triples \((X, \alpha,e)\) with \(X,e\) polarized K3 surface and \(\alpha\) basis for \(H_2(X,Z)\); \(f_e\) is connected with the product of non 0 eigenvalues of the Laplacian \(\Delta^{(0,1)}\) acting on smooth (0,1)-forms. In the present paper, the authors go through the construction of \(f_e\) and provide some evidence that it has a product formula and other properties analogue to the properties of \(\eta (\tau)\).
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 11F20
zbMATH DE Number: 817762
zbMATH Keywords: Dedekind's eta function
zbMATH Keywords: K3 surfaces
author: Jay Jorgenson
author: Andrey N. Todorov
MaRDI profile type: Publication
full work available at URL: mrl.1995.v2.n3.a13
OpenAlex ID: W2324390152
DOI: 10.4310/MRL.1995.V2.N3.A13
description: scientific article; zbMATH DE number 817762