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We study linear series on curves inducing injective morphisms to projectivespace, using zero-dimensional schemes and cohomological vanishings. Albeitprojections of curves and their singularities are of central importance inalgebraic geometry, basic problems still remain unsolved. In this note, westudy cuspidal projections of space curves lying on irreducible quadrics (inarbitrary characteristic).

Injective linear series of algebraic curves on quadrics