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A ð0; aÞ-geometry, a d 3, fully embedded in AGðn; qÞ is always a linear representation [2]. In [4] the ð0; 2Þ-geometries fully embedded in AGð3; qÞ are classified up to linear representations. Here we extend this result to full embeddings in AGðn; qÞ. As a corollary we classify the semipartial geometries with a > 1 fully embedded in AGðn; qÞ, but not as a linear representation.

In De Clerck and Delanote (Des. Codes Cryptogr, 32:103-110, 2004) it is shown that if a (0, alpha) -geometry with alpha >= 3 is fully embedded in AG (n, q) then it is a linear representation. In De Feyter (J. Combin Theory Ser A, 109(t): 1-23, 2005; Discrete math, 292:45-54,2005) the (0, 2)-geometries fully embedded in AG(3, q) are classified apart from two open cases. In this paper, we solve these two open cases. This classification for AG (3, q) is used in De Feyter (Adv Geom, 5: 219-292, 2005) to classify the (0, 2)-geometries fully embedded in AG(n, q)

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