Additive Actions on Toric Projective Hypersurfaces

Term Paper Almost-toric Projective Hypersurfaces

Almost-toric projective hypersurfaces could be parameterized by n+2 monomials in n variables multiplying univariate polynomials in an extra variable. In this paper we give a combinatorial description of the Newton polytope (actually it’s a polygon) of the defining polynomial of almosttoric hypersurfaces.

Some Observations on Local and Projective Hypersurfaces

Let R be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules (M, N) over R we study applications of rigidity of Tor(M, N), based on ideas by Huneke, Wiegand and Jorgensen. We then focus on the hypersurfaces with isolated singularity and even dimension, and show that modules over such rings behave very much like those over regular local rings. Connecti...

On a family of projective toric varieties

By means of suitable sequences of graphs, in a previous paper, we have studied the reduced lexicographic Gröbner bases of a family of homogeneous toric ideals. In this paper, we deepen the analysis of those bases and derive some geometric properties of the corresponding projective toric varieties.

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.

Smooth Divisors of Projective Hypersurfaces