Birational maps of X(1) into P^2 (CROSBI ID 201165)
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Muić, Goran ; Mikoč, Damir
engleski
Birational maps of X(1) into P^2
Birational maps of modular curve X (1) attached to SL(2, Z) into the projective plane are studied in the paper. It is shown that every curve of genus 0 and degree q in the projective plain can be uniformized by modular forms for SL(2, Z ) of weight 12q but not with modular forms of smaller weight, and that the corresponding uniformization can be chosen to be a birational equivalence. Other regular maps from X(1) into the projective plane are studied, and the equation of obtained projective curve is computed in the paper. Numerical examples are provided in SAGE.
projective plane; algebraic curves; birational maps; uniformization
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