Even-homogeneous supermanifolds on the complex projective line

We obtain the classification of even-homogeneous non-split complex supermanifolds of dimension 1|m, m⩽3, on CP1, up to isomorphism. For m=2, we show that there exists only one such supermanifold, which is the superquadric in CP2|2 constructed independently by P. Green (1982) [4] and V.P. Palamodov (1987) [1]. For m=3, we prove that there exists a series of non-split even-homogeneous supermanifolds, parameterized by elements in Z×Z, three series of non-split even-homogeneous supermanifolds, parameterized by elements of Z, and finite set of exceptional supermanifolds.