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

ISBN-10: 1402000057

ISBN-13: 9781402000058

ISBN-10: 9401010110

ISBN-13: 9789401010115

An updated document at the present prestige of vital learn issues in algebraic geometry and its functions, comparable to computational algebra and geometry, singularity concept algorithms, numerical strategies of polynomial platforms, coding concept, communique networks, and machine imaginative and prescient. Contributions on extra basic points of algebraic geometry contain expositions on the topic of counting issues on forms over finite fields, Mori concept, linear platforms, Abelian types, vector bundles on singular curves, degenerations of surfaces, and replicate symmetry of Calabi-Yau manifolds.

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

**Example text**

Let C be a non degenerate disjoint union of s distinct irreducible smooth curves C 0/ the same genus g. resp. of degree d i • and with Oc,(t) non special. )! t > O. Let d = 'LJ= I d i and = min {t E N\ ('~n) > dt + s( 1 - g) }. Let V/ be a set of # + 1 distinct points ~fC and V, = UV/' Let Gt be the matrix whose columns are the vectors of the evaluations of the terms of degree t over the points of v,. +s(l-g). Moreover. i/gl, ... ,ge is a basis for J(C)a and Ha+1 is the matrix whose columns are the vectors of the coefficients of Xigj (for every i = 0, ...

In a previous paper, at the same time and independently from Bayle and Beauville, the author of the present contribution showed how to emend and to improve Castelnuovo and Enriques' techniques in order to complete their "proof' of birational classification of rational double planes. We stress the fact that the argument we used is algorithmic and constructive, while the proof of Bayle and Beauville relies on the Mori cone theorem, which is theoretical in nature. C. project EAGER, contract n. HPRN-CT-2000-00099.

Physics and Computation, 23-35. © 2001 Kluwer Academic Publishers. L. CHIANTINI, F. CIOFFI AND F. ORECCHIA 24 rank are characterized by means of the Hilbert function; moreover results about the number of minimal generators for such unions of rational curves are described. e. of curves C whose index of speciality ec := max{ tlHI (Odt)) =I O} is null. 1). So, recall that a point [yo : ... : Yn] of IPR is a "rational point" over K if there exist Yo'''' ,)~. of K such that [yo : ... : Yr] = [VO : ...

### Applications of Algebraic Geometry to Coding Theory, Physics and Computation by I. Burban, Yu. Drozd, G.-M Greuel (auth.), Ciro Ciliberto, Friedrich Hirzebruch, Rick Miranda, Mina Teicher (eds.)

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