We show that the log canonical bundle, κ, of M0,n is very ample, show the homogeneous coordinate ring is Koszul, and give a nice set of rank 4 quadratic generators for the homogeneous ideal: The embedding is equivariant for the symmetric group, and the image lies on many Segre embedded copies of P×· · ·×P, permuted by the symmetric group. The homogeneous ideal of M0,n is the sum of the homogene...

We show that the log canonical bundle, κ, of M0,n is very ample, show the homogeneous coordinate ring is Koszul, and give a nice set of rank 4 quadratic generators for the homogeneous ideal: The embedding is equivariant for the symmetric group, and the image lies on many Segre embedded copies of P×· · ·×P, permuted by the symmetric group. The homogeneous ideal of M0,n is the sum of the homogene...

It is well known that the degree of a 2m-variable bent function is at most m. However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree m in 2m variables when m > 3; there is no homogenous bent function of degree m− 1 in 2m variables when m > 4; Generally, for any nonnegative integer k, there exists a positive...

We determine all homogeneous pseudo-embeddings of the affine space AG(n, 4) and the projective space PG(n, 4). We give a classification of all pseudo-hyperplanes of AG(n, 4). We also prove that the two homogeneous pseudo-embeddings of the generalized quadrangle Q(4, 3) are induced by the two homogeneous pseudo-embeddings of AG(4, 4) into which Q(4, 3) is fully embeddable.