Surfaces of general type with canonical map degree d bigger than 8 have bounded geometric genus and irregularity. In particular the irregularity is at most 2 if d≥10. present paper, existence surfaces = 10 all possible irregularities, 12 1 2, 14 0 proven, by constructing these as Z23-covers certain rational surfaces. These results together construction C. Rito a surface show that possibilities ...

The theorem is the best possible in the sense that the components of nonsingular algebraic subsets in the conclusion cannot be replaced by nonsingular algebraic subsets (see Remark 14). It is well known that the topology of the singularities of 7/2-homology cycles is closely related to real algebraic structures on V [AK 2, AK3]. Therefore it is natural to study to what extent general homology c...

We prove that any holomorphic codimension 1 foliation on the complex projective plane has at most one singularity up to action of an ad-hoc birational map. Consequently, algebraic affine no singularities a suitable self map into itself.

In this note we show how to test whether or not certain algebraic equations derived in the paper Fault Detection and Isolation for State Affine Systems, are solvable and to describe a solution method. Test and solution rely upon elementary linear algebraic techniques.

Budaghyan and Carlet [4] constructed a family of almost perfect nonlinear (APN) hexanomials over a field with r2 elements, and with terms of degrees r + 1, s + 1, rs+ 1, rs+ r, rs+ s, and r + s, where r = 2m and s = 2n with GCD(m,n) = 1. The construction requires a certain technical condition, which was verified empirically in a finite number of examples. Bracken, Tan, and Tan [1] proved the co...

In this paper we determined explicitly the multiplicative inverses of the Dobbertin and Welch APN exponents in Z2n−1, and we described the binary weights of the inverses of the Gold and Kasami exponents. We studied the function Invd (n), which for a fixed positive integer d maps integers n ≥ 1 to the least positive residue of the inverse of d modulo 2n − 1, if it exists. In particular, we showe...