Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis (Encyclopaedia of Mathematical Sciences, 74) - Hardcover

Hardcover

ISBN 10: 3540562591 ISBN 13: 9783540562597

Publisher: Springer, 1994

Synopsis

Of making many books there is no end; and much study is a weariness of the flesh. Eccl. 12.12. 1. In the beginning Riemann created the surfaces. The periods of integrals of abelian differentials on a compact surface of genus 9 immediately attach a g­ dimensional complex torus to X. If 9 ~ 2, the moduli space of X depends on 3g - 3 complex parameters. Thus problems in one complex variable lead, from the very beginning, to studies in several complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates Z 1, ... , Zn; holomorphic functions are, locally, those functions which are holomorphic in these coordinates. th In the second half of the 19 century, classical algebraic geometry was born in Italy. The objects are sets of common zeros of polynomials. Such sets are of finite dimension, but may have singularities forming a closed subset of lower dimension; outside of the singular locus these zero sets are complex manifolds.

About this title

Language Notes

Text: English (translation)
Original Language: Russian

Edition details

• Publisher: Springer
• Publication date: 1994
• Language: English
• ISBN 10: 3540562591
• ISBN 13: 9783540562597
• Binding: Hardcover
• Number of pages: 380
• Editor: Grauert H., Peternell Thomas, Remmert R.