an:01802560
Zbl 1058.14054
Homma, Masaaki; Ohbuchi, Akira
Plane curves with aligned conductors
EN
Far East J. Math. Sci. (FJMS) 4, No. 1, 21-53 (2002).
00085020
2002
j
14H50 14H45 14H51
birationally very ample; theory of adjoint curves
Summary: An invariant toward a classification of curves \(X\) with a birationally very ample and special invertible sheaf \(L\) is proposed, and an extremal pair \((X, L)\) by means of the invariant is a smooth plane curve \(X\) with \(O_X(1)\) corresponding line sections and vice versa. For pairs \((X, L)\) next to extremal ones, all but one exception is characterized by the image \(\phi_L(X)\) to be a plane singular curve with aligned conductors. The heart of the paper is to study such a singular plane curve with its normalization involving projective geometry and the theory of adjoint curves.