# Analysis and Geometry in Several Complex Variables (Trends - download pdf or read online

By Gen Komatsu, Masatake Kuranishi

ISBN-10: 0817640673

ISBN-13: 9780817640675

This quantity is an outgrowth of the fortieth Taniguchi Symposium research and Geometry in numerous complicated Variables held in Katata, Japan. Highlighted are the latest advancements on the interface of complicated research and genuine research, together with the Bergman kernel/projection and the CR constitution. the gathering additionally contains articles exploring mathematical interactions with different fields resembling algebraic geometry and theoretical physics. This paintings will function a superb source for either researchers and graduate scholars attracted to new tendencies in a few diverse branches of study and geometry.

**Read or Download Analysis and Geometry in Several Complex Variables (Trends in Mathematics) PDF**

**Similar differential geometry books**

**The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan, Alan W. Reid PDF**

For the previous 25 years, the Geometrization application of Thurston has been a motive force for examine in 3-manifold topology. This has encouraged a surge of job investigating hyperbolic 3-manifolds (and Kleinian groups), as those manifolds shape the biggest and least well-understood type of compact 3-manifolds.

**Elegant chaos. Algebraically simple chaotic flows - download pdf or read online**

This seriously illustrated e-book collects in a single resource lots of the mathematically basic structures of differential equations whose strategies are chaotic. It comprises the traditionally very important platforms of van der Pol, Duffing, Ueda, Lorenz, RÃ¶ssler, and so forth, however it is going directly to convey that there are numerous different platforms which are less complicated and extra stylish.

**Download PDF by David Bachman: A geometric approach to differential forms**

This article offers differential types from a geometrical standpoint obtainable on the undergraduate point. It starts with easy thoughts comparable to partial differentiation and a number of integration and lightly develops the complete equipment of differential types. the topic is approached with the concept advanced techniques will be equipped up through analogy from easier instances, which, being inherently geometric, usually might be top understood visually.

- Differential Geometry of Frame Bundles
- The Ricci Flow: Techniques and Applications: Geometric Aspects (Mathematical Surveys and Monographs) (Pt. 1)
- Geometrie [Lecture notes]
- Loop Spaces, Characteristic Classes and Geometric Quantization (Modern Birkhäuser Classics)

**Extra resources for Analysis and Geometry in Several Complex Variables (Trends in Mathematics) **

**Sample text**

A very simple example is provided by the product of two curves, one elliptic and the other of genus > 2. Of course, the surface in this example has the algebraic dimension 2. In order to give some other examples of properly elliptic surfaces, consider again principal elliptic fibre bundles X over a curve B of genus > 2, given by ~ ~ H I ( B , EB) with c(~) ~ 0. 34 that b~(X) is odd, so X is non-k/ihlerian, hence a(X) = 1. Clearly, we have kod(X) = 1. (10) A surface of general type is a surface with kod(X) = 2.

In particular, it follows a(X) > 1. 36 2. 15 Let X be a nonalgebraic surface with a(X) = O. Then: (i) h~ h~ (2) hl,~ <_ 1 for any line bundle L E Pic(X); in particular pg(X) 02x) <_ 1; := dime H~ g2}) _< 2. Proof. (1) If 81 and s2 are two linearly independent (over r sections of the line bundle L, then st~s2 is a (global) meromorphic function on X which is not constant. It follows a(X) > 1, contradiction. (2) Let cot, w2 and Caa be three linearly independent holomorphic 1-forms on X. Then cot Acoz and wt Awa are not identically zero on X, otherwise it would follow a(X) > 1 (see the previous remark).

Then any irreducible curve on X is contained in some fibre and thus the fibration is unique. Proof. Let D be an irreducible curve contained in no fibre and let x0 E D be a point on D. D > 0. 10. Let X be a compact surface. IV , Prop. 1). In particular, it follows a(X) > 1. 36 2. 15 Let X be a nonalgebraic surface with a(X) = O. Then: (i) h~ h~ (2) hl,~ <_ 1 for any line bundle L E Pic(X); in particular pg(X) 02x) <_ 1; := dime H~ g2}) _< 2. Proof. (1) If 81 and s2 are two linearly independent (over r sections of the line bundle L, then st~s2 is a (global) meromorphic function on X which is not constant.

### Analysis and Geometry in Several Complex Variables (Trends in Mathematics) by Gen Komatsu, Masatake Kuranishi

by Brian

4.4