Clifford’s inequality for real algebraic curves. (English) Zbl 1063.14074
The classical Clifford’s inequality, which, for complex curves, bounds from above the dimension of a special linear system by half of the degree, is refined for real algebraic curves under certain assumptions. For example, the Clifford’s upper bound reduces by half of the number of real branches, containing an odd number of points of a given divisor, provided, that the total number of real branches is at least the genus of the curve. A few new bounds for the number of ovals (null-homologous real branches) of real space curves are deduced.
Reviewer: Eugenii I. Shustin (Tel Aviv)
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