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.

Metrics on Calabi-Yau manifolds are used to derive a formula that finds the existence of integer solutions to polynomials. These metrics are derived from an associated algebraic curve, together with its anti-holomorphic counterpart. The integer points in the curve coincide with points on the manifold, and the metric form around these points are used to find their existence. The explicit form of...

We analyze the algebraic and geometric structures of deformations of Schwarz type topological field theories. Deformations of the Chern-Simons-BF theory and BF theories in n dimensions are analyzed. Two dimensionanl theory induces the Poisson structure and three dimensional theory induces the Courant algebroid structure on the target space as a sigma model. We generalize these structures to hig...