Let S be a smooth algebraic surface in P-3 (C). Movasati and Sertoz (Rend. Circ. Mat. Palermo 2:1-17, 2020) associate an ideal I-alpha(C) to the primitive cohomology class alpha(C) of C in S. We show that the equations of C can be determined by I-alpha(C) under numerical conditions. We apply this result to reconstruct rational curves and arithmetically CohenMacaulay curves from their cohomology classes. On the other hand, we show that the class alpha(C) of a rational quartic curve C on a smooth quartic surface S is not even perfect, that is, that I-alpha(C) is bigger than the sum of the Jacobian ideal of S and of the homogeneous ideals of curves D in S for which I-alpha(D) = I-alpha(C).
Reconstructing curves from their Hodge classes
Pirola G. P.;
2023-01-01
Abstract
Let S be a smooth algebraic surface in P-3 (C). Movasati and Sertoz (Rend. Circ. Mat. Palermo 2:1-17, 2020) associate an ideal I-alpha(C) to the primitive cohomology class alpha(C) of C in S. We show that the equations of C can be determined by I-alpha(C) under numerical conditions. We apply this result to reconstruct rational curves and arithmetically CohenMacaulay curves from their cohomology classes. On the other hand, we show that the class alpha(C) of a rational quartic curve C on a smooth quartic surface S is not even perfect, that is, that I-alpha(C) is bigger than the sum of the Jacobian ideal of S and of the homogeneous ideals of curves D in S for which I-alpha(D) = I-alpha(C).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
