show/hide this revision's text 4 edited body

As for a result that was not simply incorrectly proved, but actually false, there is the case of the Severi bound(*) for the maximum number of singular double points of a surface in P^3. The prediction implies that there are no surfaces in P^3 of degree 6 with more than 52 nodes, but in fact there are such surfaces in P^3 with 64 nodes (and this is optimal).

(*) Francesco Severi; "Sul massimo numero di nodi di una superficie di dato ordine dello spazio ordinario o di una forma di un operspazio.iperspazio." Ann. Mat. Pura Appl. (4) 25, (1946). 1--41.
show/hide this revision's text 3 Added explicit reference

As for a result that was not simply incorrectly proved, but actually false, there is the case of the Severi bound(*) for the maximum number of singular double points of a surface in P^3. The prediction implies that there are no surfaces in P^3 of degree 6 with more than 52 nodes, but in fact there are such surfaces in P^3 with 64 nodes (and this is optimal).

(*) Francesco Severi; "Sul massimo numero di nodi di una superficie di dato ordine dello spazio ordinario o di una forma di un operspazio." Ann. Mat. Pura Appl. (4) 25, (1946). 1--41.
show/hide this revision's text 2 added 16 characters in body; added 4 characters in body

As for a result that was not simply incorrectly proved, but actually false, there is the case of the Severi bound for the maximum number of singular double points of a surface in P^3. The prediction implies that there are no surfaces in P^3 of degree 6 with more than 52 nodes, but actually in fact there are such surfaces in P^3 with 64 nodes (and this is optimal).
show/hide this revision's text 1