By I. Burban, Yu. Drozd, G.-M Greuel (auth.), Ciro Ciliberto, Friedrich Hirzebruch, Rick Miranda, Mina Teicher (eds.)

An up to date record at the present prestige of vital examine themes in algebraic geometry and its functions, similar to computational algebra and geometry, singularity idea algorithms, numerical recommendations of polynomial platforms, coding thought, conversation networks, and laptop imaginative and prescient. Contributions on extra basic elements of algebraic geometry comprise expositions relating to counting issues on kinds over finite fields, Mori thought, linear platforms, Abelian forms, vector bundles on singular curves, degenerations of surfaces, and replicate symmetry of Calabi-Yau manifolds.

**Read Online or Download Applications of Algebraic Geometry to Coding Theory, Physics and Computation PDF**

**Similar geometry books**

**Geometry of Knowledge for Intelligent Systems**

The booklet is at the geometry of agent wisdom. the $64000 thought studied during this ebook is the sphere and its Geometric illustration. To boost a geometrical photo of the gravity , Einstein used Tensor Calculus yet this is often very assorted from the information tools used now, as for example ideas of information mining , neural networks , formal thought research ,quantum computing device and different subject matters.

**Affine Maps, Euclidean Motions and Quadrics (Springer Undergraduate Mathematics Series)**

Affine geometry and quadrics are interesting topics by myself, yet also they are vital functions of linear algebra. they provide a primary glimpse into the realm of algebraic geometry but they're both suitable to a variety of disciplines equivalent to engineering.

This textual content discusses and classifies affinities and Euclidean motions culminating in category effects for quadrics. A excessive point of aspect and generality is a key characteristic unequalled by way of different books to be had. Such intricacy makes this a very available instructing source because it calls for no time beyond regulation in deconstructing the author’s reasoning. the availability of a giant variety of workouts with tricks may help scholars to strengthen their challenge fixing abilities and also will be an invaluable source for teachers whilst environment paintings for autonomous study.

Affinities, Euclidean Motions and Quadrics takes rudimentary, and sometimes taken-for-granted, wisdom and offers it in a brand new, finished shape. usual and non-standard examples are verified all through and an appendix presents the reader with a precis of complicated linear algebra proof for fast connection with the textual content. All elements mixed, this can be a self-contained publication perfect for self-study that isn't merely foundational yet targeted in its strategy. ’

This textual content can be of use to teachers in linear algebra and its functions to geometry in addition to complicated undergraduate and starting graduate scholars.

**Normal forms and bifurcation of planar vector fields**

This ebook is especially interested by the bifurcation concept of ODEs. Chapters 1 and a couple of of the ebook introduce systematic tools of simplifying equations: heart manifold conception and basic shape conception, in which one could decrease the size of equations and alter types of equations to be so simple as attainable.

- Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces
- Geometry and physics
- Divided spheres. Geodesics and the orderly subdivision of the sphere
- The Glorious Golden Ratio
- Foundations of Differential Geometry (Wiley Classics Library) (Volume 2)
- Guide to Computational Geometry Processing: Foundations, Algorithms, and Methods

**Additional resources for Applications of Algebraic Geometry to Coding Theory, Physics and Computation**

**Example text**

Over a field K of characteristic y~, ... ,y:. of K such that 30 L. CHIANTINI, F. CIOFFI AND F. 1 ) where A 1= 0, 1, see (Silverman, III, Prop. 7). 1) is a Weierstrass representation of an elliptic plane curve in the Legendre form. The condition A 1= 0, 1 is equivalent to the fact that E is smooth, see for example (Silverman and Tate, IV, section 3). We suppose that A E K. Every field K contains a copy of Q or of Z p for some prime p and so we can assume that K = Q or Z p' To study an algebraic object over Q it is useful to study the reduction of the object modulo primes.

Hence, the maximal rank and the minimal generation of such curves are studied. In particular, we consider elliptic curves and we describe a method to compute their Hilbert functions in any dimension and for every choice of the degrees. Applications to the study of elliptic curves on threefolds are shown. Key words: Elliptic curves, Hilbert function. Mathematics Subject Classification (2000): 14H52, 14Q05. 1. Introduction In this paper we study the maximal rank and the minimal generation of disjoint unions of distinct non special curves, with applications to elliptic curves.

2. The Segre Conjecture ,2 Let PI, ... , Pn be general points in the complex projective plane and let m I, ... , mn be positive integers. We let ~J be the linear system of plane curves of degree d and ~ (p';ll .... , p;;lll) the sub-linear system of ~ of curves having multiplicity at least mj at the point Pi, i = 1, ... , n. ( /111 11111) Pi! ~PI ""'P/1' Let 1t : S -+ JlD2 be the blow-up of JlD2 at the points PI, ... ,Pn. Let £ be a line bundle on S, or, by abusing notation, the corresponding complete linear system.