Good eggs and Veronese varieties

We give a new proof of the main theorem of Thas (J. Combin. Theory Ser. A 79 (1997) 223-254) concerning the connection between good eggs in PG(4n-1,q), q odd, and Veronese varieties, using the model for good eggs in PG(4n-1,q), q odd, from Lavrauw and Penttila (J. Combin. Theory Ser. A 96(2) (2001) 303-315).