Via the correspondence between algebraic curves and floor diagrams [BM09, Theorem 2.

To enumerate algebraic curves with floor diagrams we need the notion of markings of such diagrams.

5) we first look for the branch of the

algebraic curve [[PSI].

Then whether we can get an

algebraic curve by all edges in a map or by make operations on the vertices or edges of the map to get plane

algebraic curve with given k-multiple points?

DEMMEL, Algorithms for intersecting parametric and

algebraic curves I.

Their topics include Newton trees at infinity of

algebraic curves, group actions on affine cones, holomorphic curves on irregular varieties of general type starting from surfaces, equivariant derivations and additive group actions, and embeddings of hyperbolas.

This graduate textbook introduces the theory of error-correcting codes, working over an arbitrary finite field;

algebraic curves, working over an algebraically closed field; geometry over a finite field; and constructions of algebraic geometry codes.

Six talks were selected from seminars at the GANITA Lab 2001-08 to represent the treatment of point counting and arithmetic on

algebraic curves and Abelian varieties over finite fields at the facility devoted to studying the application of mathematics to problems in information technology.

Other topics include contour correspondence via ant colony optimization, visualization of implicit

algebraic curves, real-time breaking waves for shallow water simulations, and image-space caustics and curvatures.

Twenty papers from the June 2004 meeting present recent research on

algebraic curves, Riemann surfaces, modular forms, and hyperbolic geometry.

Papers on coding theory look at topics such as coding theory applications of Groobner bases, methods of computing parameters of codes corresponding to

algebraic curves, and problems in the theory of designs.