Delle superfìcie d' ordine 6 o 7 con infinite cubiche piane razionali 



13 



Per il presente caso basta ripetere la costruzione del n° 48 sopprimendo la retta dop- 

 pia d. 



52. Sia 3' = 3" = x =■ o, p c — 6. 



Una superficie siffatta è stata ottenuta al n° 6. 



53. Indicando con 



pi , s, 3', 3". x), (n, pi , s, 3', 3", x\ , pi , s, 3', 3" x)' 



la superficie y secondo che n è gobbo, ovvero (ir) inviluppa un cono il cui vertice non è 



punto base di (k), o infine {k) ha un (solo) punto base, possiamo concludere che : 



le superficie dell' S 3 , d'ordine n = 6 o n = 7 con un fascio di cubiche piane razionali i 



cui piani non costituiscono un fascio sono ; 



per n = 6 : 



(3,0,1,0,0,0/; (2,0,1,0,0,3)'; (2,0,1,1,0,2)'; (2,0,1,0,1,0)'; (2,0,1,0,0,2),; (2,0,1,0,0,2)'; 

 (2,0,1,1,0,1),; (2,0,1,1,0,1)'; (2,0,1,2,0,0/; (2,0,1,0,0,1),; (2,0,1,1,0,0)'; (2,0,1,0,0,0)'. 



per n — 7 : 



(3,0,1,0,0,2)': (3,0,1,1,0,1)'; (3,0,1,1,0,0)'; (3,0,1,0,0,0)'; (2,0,1,0,0,5)'; (2,0,1,1,0,4)'; 



(2,0,1,2,0,3)'; (2,0,1,0,1,2)'; (2,0,1,1,1,1)'; (2,0,1,0,0,4),; (2,0,1,0,0,4)'; (2,0,1,1,0,3),; 



(2,0,1,1,0,3)'; (2,0,1,2,0,2)!; (2,0,1,2,0,2/; (2,0,1,3,0,1),; (2,0,1,3,0,1)'; (2,0,1,1,1,0)'; 



(2,0,1,0,0,3),; (2,0,1,0,0,3)'; (2,0,1,1,0,2),; (2,0,1,1,0,2)'; (2,0,1,0,1,0)'; (2,0,1,0,0,2),; 



(2,0,1,0,0,2)'; (2,0,1,1,0,1),; (2,0,1,2,0,0)'; (2,0,1,1,0,0)'; (2,0,1,0,0,1),; (2,0,1,0,0,0)'. 



Catania, luglio 1917. 



