A smooth irreducible plane projective curve of degree d has geometric genus g = (d−1)(d−2)/2. Quadrics have g=0 (rational), cubics have g=1 (elliptic), quartics have g=3 (canonical), quintics have g=6. Derived from Riemann-Roch with K_C…
A smooth irreducible plane projective curve of degree d has geometric genus g = (d−1)(d−2)/2. Quadrics have g=0 (rational), cubics have g=1 (elliptic), quartics have g=3 (canonical), quintics have g=6. Derived from Riemann-Roch with K_C…