A division theorem for nodal projective hypersurfaces

Pseudo Ricci symmetric real hypersurfaces of a complex projective space

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

The Second Main Theorem of Hypersurfaces in the Projective Space

Hyperbolicity of Nodal Hypersurfaces

We show that a nodal hypersurface X in P3 of degree d with a sufficiently large number l of nodes, l > 8 3 (d2 − 5 2 d), is algebraically quasi-hyperbolic, i.e. X can only have finitely many rational and elliptic curves. Our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in famil...

A helly type theorem for hypersurfaces

Let r be a commutative field (finite or infinite) and let P = P(n, r) be the n-dimensional projective space over ZY Then every point x E P can be expressed by n + 1 homogene coordinates x = (x,,..., x,), not all zero and (x0,..., x,) = @x0,..., Ax,) for OflET. By a hypersurface of degree d we simply mean the set of all points x E P with p(x) = 0, where p(x) is a homogenous polynomial of degree ...

Smooth Divisors of Projective Hypersurfaces