Download PDF by Voisin C.: Hodge theory and complex algebraic geometry 1

By Voisin C.

ISBN-10: 0521802601

ISBN-13: 9780521802604

Show description

Read or Download Hodge theory and complex algebraic geometry 1 PDF

Best algebraic geometry books

Lectures on introduction to moduli problems and orbit spaces - download pdf or read online

Backbone identify: creation to moduli difficulties and orbit areas.

Download e-book for iPad: Higher-Dimensional Algebraic Geometry by Olivier Debarre

Higher-Dimensional Algebraic Geometry reviews the type concept of algebraic forms. This very energetic quarter of study remains to be constructing, yet an awesome volume of information has gathered over the last 20 years. The author's objective is to supply an simply available advent to the topic.

Download PDF by Constance Reid: Hilbert

Now in new exchange paper variations, those vintage biographies of 2 of the best twentieth Century mathematicians are being published below the Copernicus imprint. those noteworthy bills of the lives of David Hilbert and Richard Courant are heavily similar: Courant's tale is, in lots of methods, visible because the sequel to the tale of Hilbert.

Paolo Cascini, James McKernan, Jorge Vitório Pereira's Foliation Theory in Algebraic Geometry PDF

That includes a mix of unique study papers and accomplished surveys from a world workforce of prime researchers within the thriving fields of foliation concept, holomorphic foliations, and birational geometry, this ebook offers the complaints of the convention "Foliation thought in Algebraic Geometry," hosted by way of the Simons starting place in long island urban in September 2013.

Additional resources for Hodge theory and complex algebraic geometry 1

Example text

Let U be an open set of X such that there exists a non-zero section χ of E over U, and a submersive map φ : U → Rn−1 whose fibres are the trajectories of χ . By the flow-box theorem, we may assume that U is diffeomorphic to V × (0, 1) where V is an open set of Rn−1 , that φ is the first projection and that χ is identified with ∂t∂ . We will show the following result. 21 The integrability condition implies that there exists a distribution F of rank k − 1 on V such that E = (φ∗ )−1 (F). Moreover, E satisfies the integrability condition if and only if F does.

5 at every point of U . 7 If f is holomorphic and does not vanish on U , then 1f is holomorphic. Similarly, if f, g are holomorphic, f g and f + g and g ◦ f (when g is defined on the image of f ) are all holomorphic. Proof The map z → 1z is holomorphic on C∗ , so that the first assertion follows from the last one. Furthermore, if g and f are C 1 and g is defined on the image of f , then g ◦ f is C 1 and we have d(g ◦ f )u = dg f (u) ◦ d f u . 24 1 Holomorphic Functions of Many Variables If dg f (u) and d f u are both C-linear for the natural identifications of TC,u , TC, f (u) and TC,g◦ f (u) with C, then d(g ◦ f )u is also C-linear, and the last assertion is proved.

E. a holomorphic vector subbundle of rank k of the holomorphic tangent bundle TX . Then E is integrable in the holomorphic sense if and only if we have the integrability condition [E, E] ⊂ E. Here, the integrability in the holomorphic sense means that X is covered by open sets U such that there exists a holomorphic submersive map φU : U → Cn−k satisfying E u = Ker φ∗ : TU,u → TCn−k ,φ(u) for every u ∈ U . Proof We first reduce to the real Frobenius theorem, by noting that the conditions that E is holomorphic and that [E, E] ⊂ E imply that the real distribution E ⊂ TX,R also satisfies the Frobenius integrability condition, and thus is integrable.

Download PDF sample

Hodge theory and complex algebraic geometry 1 by Voisin C.


by Charles
4.3

Rated 4.56 of 5 – based on 42 votes

Categories: Algebraic Geometry