Mixed cusp forms and holomorphic forms on elliptic varieties
type: Item
instance of: scholarly article
title: Mixed cusp forms and holomorphic forms on elliptic varieties
zbMATH Open document ID: 0648.14017
author: Min Ho Lee
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pjm/1102689686
review text: Let \(E^m\) be an elliptic variety, that means the resolution of the singularities of the \(m\)-times fibre product \(E\times_{\pi}\dots\times_{\pi}E\to X\) of an elliptic fibration \(\pi: E\to X\). The author generalizes the results for elliptic surface \((m=1)\) [see \textit{B. Hunt} and \textit{W. Meyer}, Math. Ann. 271, 53--80 (1985; Zbl 0533.14019)] by defining mixed cusp forms associated to \(E^m\) and proving that the space of these mixed cusp forms coincides with the space of holomorphic \((m+1)\)-forms on \(E^m\). Thus he succeeds in determining the geometric genus of \(E^m\) under certain conditions.
Mathematics Subject Classification ID: 11F12
Mathematics Subject Classification ID: 14J40
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 4057671
zbMATH Keywords: elliptic variety
zbMATH Keywords: mixed cusp forms
zbMATH Keywords: geometric genus
MaRDI profile type: Publication
OpenAlex ID: W2028711050
cites work: On automorphic forms and Hodge theory
cites work: Mixed automorphic forms and invariants of elliptic surfaces
cites work: On compact analytic surfaces. III
cites work: On Rational Singuarities
cites work: On elliptic modular surfaces
cites work: HOLOMORPHIC DIFFERENTIAL FORMS OF HIGHER DEGREE ON KUGA’S MODULAR VARIETIES
cites work: THE STUDY OF THE HOMOLOGY OF KUGA VARIETIES
cites work: SHIMURA INTEGRALS OF CUSP FORMS
DOI: 10.2140/PJM.1988.132.363
description: scientific article; zbMATH DE number 4057671