By A.N. Parshin (editor), I.R. Shafarevich (editor), I. Rivin, V.S. Kulikov, P.F. Kurchanov, V.V. Shokurov

ISBN-10: 3540546812

ISBN-13: 9783540546818

This two-part EMS quantity presents a succinct precis of complicated algebraic geometry, coupled with a lucid creation to the new paintings at the interactions among the classical zone of the geometry of advanced algebraic curves and their Jacobian forms. a very good spouse to the older classics at the topic.

**Read or Download Algebraic geometry 03 Complex algebraic varieties, Algebraic curves and their Jacobians PDF**

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**Additional resources for Algebraic geometry 03 Complex algebraic varieties, Algebraic curves and their Jacobians**

**Example text**

These sections are devoted to summarizing the results presented in the chapter and so as to present some open problems. Also we include some bibliographical references which could be useful for extending the study of the topics covered. Chapter 2 EUCLIDEAN POSITION If we try to compute the convex hull or a triangulation of a set of sites in a surface and all those sites are very elose to each other, we can intuitively think that planar methods will be valid in this situation. This intuition has been used on several occasions by many authors, but sometimes it is not elear what 'very elose to each other' means.

3. CYLINDRICAL POSITION IN THE TORUS In the case of the torus, in addition to Euclidean position we have another situation in which we can apply directIy some methods obtained in this book for the cylinder. So we will say that a set of sites on this surface is in cylindrical position if the set of them is contained between two opposite parallels or two opposite meridians. Obviously, if a set is in Euclidean position it is in cylindrical position as weIl, but, of course, the converse is not true in general.

20. 53 The shaded region must be contained in Cm(P) ALGORITHM CH-CONE(P) INPUT: P = {Vl, V2, ... , VN} set OUTPUT: Metrically convex hull 0/ points on the cone. 0/ P on the cone. 1/ P is in Euclidean position go to Step 3. STEP 2 Compute the convex hull 0/ ifJ-l(p) in X adapting a planar convex hull algorithm. The m-convex hull 0/ P is STEP 1 CH(ifJ-l(p)) n C2 • (END) 3 Compute the convex hull 0/ P in the cone using a planar STEP convex hUll algorithm. 4. Algorithm for computing the metrically convex hull of a set on the cone.

### Algebraic geometry 03 Complex algebraic varieties, Algebraic curves and their Jacobians by A.N. Parshin (editor), I.R. Shafarevich (editor), I. Rivin, V.S. Kulikov, P.F. Kurchanov, V.V. Shokurov

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