Examples of Hilbert Modular Surfaces As an illustration of the previous chapters we now give examples. Reading this chapter will resemble a visit to a zoological garden: each of the surfaces presented here is a world in itself that can ...

Author: Gerard van der Geer

Publisher: Springer Science & Business Media

ISBN: 9783642615535

Category: Mathematics

Page: 294

View: 921

Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples - in fact a whole chapter - completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field.

[16] Hirzebruch, F. :Hilbert modular surfaces. L'Ens. Math. 19, 183-281 (1973). [17] Hirzebruch, F.: Kurven auf den Hilbertschen Modulflächen und Klassenzahl relationen. Classification of algebraic varieties and compact manifolds.

The arithmetic theory of periods of modular forms is revealing its nature as Diophantine index theorem.

Author: Takayuki Oda

Publisher: Birkhauser

ISBN: UOM:39015072702759

Category: Science

Page: 123

View: 952

The arithmetic theory of periods of modular forms is revealing its nature as Diophantine index theorem. This paper is an attempt to amplify this universal principle by discussing a special case: Hodge structures of Hilbert modular surfaces.

Hilbert modular surfaces. Erg. der Math. III/16 Springer-Verlag van der Geer, G., Zagier, D. 18. The Hilbert modular group for the field Q(V13). Invent. Math. 42, 93-133 (1977) Gundlach, K-B. 19. Some new results in the theory of ...

Author: Eberhard Freitag

Publisher: Springer Science & Business Media

ISBN: 9783662026380

Category: Mathematics

Page: 252

View: 882

Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of number theory has been given more and more attention and thus the need for a comprehensive presentation of these results, previously scattered in research journal papers, has become obvious. The main aim of this book is to give a description of the singular cohomology and its Hodge decomposition including explicit formulae. The author has succeeded in giving proofs which are both elementary and complete. The book contains an introduction to Hilbert modular forms, reduction theory, the trace formula and Shimizu's formulae, the work of Matsushima and Shimura, analytic continuation of Eisenstein series, the cohomology and its Hodge decomposition. Basic facts about algebraic numbers, integration, alternating differential forms and Hodge theory are included in convenient appendices so that the book can be used by students with a knowledge of complex analysis (one variable) and algebra.

Hilbert modular surfaces and the classification of algebraic surfaces . Invent . Math . 23 ( 1974 ) , pp . 1-29 . [ 5 ] HIRZEBRUCH , F. and D. ZAGIER . Classification of Hilbert modular surfaces , in “ Complex Analysis and Algebraic ...

Author: Gerardus Bartholomeus Maria Van der GeerPublish On: 1977

Ann . 56,58 ( 1903 ) Canonical models of surfaces of general type . Publ . Math.I.H.E.S. 42 , 171-220 ( 1973 ) G. van der Geer A. Van de Ven . On the minimality of certain Hilbert Modular Surfaces . In " Complex Analysis and Algebraic ...