By Ciro Ciliberto, E. Laura Livorni, Andrew J. Sommese

**Read Online or Download Classification of Algebraic Varieties PDF**

**Similar algebraic geometry books**

**Mathematical Aspects of Geometric Modeling**

This monograph examines intimately definite recommendations which are priceless for the modeling of curves and surfaces and emphasizes the mathematical idea that underlies those rules. the 2 imperative issues of the textual content are using piecewise polynomial illustration (this topic appears to be like in a single shape or one other in each chapter), and iterative refinement, often known as subdivision.

**Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure**

Fractal styles have emerged in lots of contexts, yet what precisely is a trend? How can one make designated the constructions mendacity inside of items and the relationships among them? This publication proposes new notions of coherent geometric constitution to supply a clean method of this widespread box. It develops a brand new notion of self-similarity known as "BPI" or "big items of itself," which makes the sphere a lot more uncomplicated for individuals to go into.

From the stories of the 1st printing of this publication, released as quantity 6 of the Encyclopaedia of Mathematical Sciences: ". .. My basic influence is of a very great booklet, with a well-balanced bibliography, suggested! "Medelingen van Het Wiskundig Genootschap, 1995". .. The authors supply right here an up-to-the-minute advisor to the subject and its major functions, together with a few new effects.

- Geometric Algebra, 1st Edition
- Spinning Tops: A Course on Integrable Systems (Cambridge Studies in Advanced Mathematics)
- Lectures on Derived Categories, Edition: version 14 Oct 2010
- Riemannsche Flächen (Springer-Lehrbuch) (German Edition)
- Rigid Analytic Geometry and Its Applications (Progress in Mathematics)
- Fukaya Categories and Picard-Lefschetz Theory (Zurich Lectures in Advanced Mathematics)

**Extra resources for Classification of Algebraic Varieties**

**Sample text**

The next dilogarithm variant we mention is the p-adic dilogarithm, studied by R. Coleman and other authors. We ﬁx a prime number p and deﬁne (p) Li2 (x) = n>0, p∤n xn . n2 (14) This function can be written as Li2 (x)−p−2 Li2 (xp ), so in the complex domain it is simply a combination of ordinary dilogarithms and of no independent interest, but because we have omitted the terms in (14) with p’s in the denominator, the power series converges p-adically for all p-adic numbers x with (p) valuation |x|p < 1.

The deﬁnition and the name, of course, come from the analogy with the Taylor series of the ordinary logarithm around 1, − log(1 − z) = ∞ n=1 zn n for |z| < 1 , which leads similarly to the deﬁnition of the polylogarithm Lim (z) = ∞ n=1 zn nm for |z| < 1, m = 1, 2, . . The relation 1 d Lim (z) = Lim−1 (z) (m ≥ 2) dz z is obvious and leads by induction to the extension of the domain of deﬁnition of Lim to the cut plane C [1, ∞); in particular, the analytic continuation of the dilogarithm is given by z Li2 (z) = − 1 0 log(1 − u) du u for z ∈ C [1, ∞) .

1]), has many other beautiful properties. In particular: (II) D(z), which is a real-valued function on C, can be expressed in terms of a function of a single real variable, namely D(z) = z 1 D +D 2 z¯ 1 − 1/z 1 − 1/¯ z +D 1/(1 − z) 1/(1 − z¯) (2) The Dilogarithm Function 11 which expresses D(z) for arbitrary complex z in terms of the function D(eiθ ) = ℑ[Li2 (eiθ )] = ∞ sin nθ . ) Formula (2) is due to Kummer. 6 4 (III) All of the functional equations satisﬁed by Li2 (z) lose the elementary correction terms (constants and products of logarithms) when expressed in terms of D(z).