Download Applications of Algebraic Geometry to Coding Theory, Physics by I. Burban, Yu. Drozd, G.-M Greuel (auth.), Ciro Ciliberto, PDF

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 up to date document at the present prestige of vital study themes in algebraic geometry and its functions, equivalent to computational algebra and geometry, singularity idea algorithms, numerical recommendations of polynomial structures, coding idea, conversation networks, and desktop imaginative and prescient. Contributions on extra primary facets of algebraic geometry comprise expositions on the topic of counting issues on kinds over finite fields, Mori idea, linear platforms, Abelian types, vector bundles on singular curves, degenerations of surfaces, and reflect symmetry of Calabi-Yau manifolds.

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

Example text

We will use the classical notions of infinitely near points, see (Enriques and Chisini; Casas-Alvero) for general theory or (Calabri) for a brief account in this setting. We denote by Ei (resp. the strict (resp. total) transform in S of the exceptional curve 0';-1 (Xi) C Si of (ji. Recall that Ei = Et - Lj %Ej in Pic(S), where % = 1 if Xi is proximate to Xi and % = 0 otherwise. In Pic(S) we may write C = 2dL - LiciEt and B = 2dL - LihiEt, where 2d = deg( C), Ci = multr , (C) and L is the total transform of a general line in jp'2.

We remark that the sextic can be reducible. The virtual branch curve of the double plane in the statement has three points of multiplicity 4. Two of them are excessive, each infinitely near of the first order to a defective double point (tacnode of the sextic) and lying on the tacnodal tangent. This type of double plane has been first described by Enriques in 1906. Later Averbuh proved that an Enriques surface is birationally equivalent to a surface that is a double plane with such a branch curve, which is a weaker result than the above statement.

And Enriques, F. (1900) Sulle eondizioni di razionalita dei piani doppi, Rend. Cire. Mat. Palermo 14,290-302. Ciliberto, C, and Paresehi, G. (1995) Pencils of minimal degree on curves on a K3 surface, 1. reine angew Math. 460, 15-36. De Franchis, M. (1904) I piani doppi dotati di due 0 pill differenziali totali di prima specie, Rend. Accad. Lincei 13,688-695. Enriques, F. ( 1896) Sui piani doppi di genere uno, Mem. Soc. Italiana delle Scienze delta dei XL 10, 201-224. Enriques, F. ( 1906) Sopra Ie superficie algebriehe di bigenere uno, Mem.

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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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