We introduce the notion of a projectively simple ring, which is an infinite-dimensional N-graded k-algebra A such that dimk A/I < ∞ for every nonzero 2-sided ideal I ⊂ A. We show that if a projectively simple ring A is strongly noetherian, is generated in degree 1, and has a point module, then A is equal in large degree to a twisted homogeneous coordinate ring B = B(X,L, σ). Here X is a smooth ...

An infinite-dimensional N-graded k-algebra A is called projectively simple if dimk A/I < ∞ for every nonzero two-sided ideal I ⊂ A. We show that if a projectively simple ring A is strongly noetherian, is generated in degree 1, and has a point module, then A is equal in large degree to a twisted homogeneous coordinate ring B = B(X,L, σ). Here X is a smooth projective variety, σ is an automorphis...

We show that the efficiency of a natural pairing between certain projectively invariant Hardy spaces on dual strongly C-linearly convex real hypersurfaces in complex projective space is measured by the norm of the corresponding Leray transform.

The projective normality of smooth, linearly normal surfaces of degree 9 in P is studied. All non projectively normal surfaces which are not scrolls over a curve are classified. Results on the projective normality of surface scrolls are also given.

The matroid terminology follows Oxley [4]. Two r×n matrices A and A′ representing the same matroid M over a field GF(q) are called projectively equivalent representations of M if one can be obtained from the other by elementary row operations and column scaling. Otherwise they are called projectively inequivalent. The matrices A and A′ are called equivalent representations of M if, in addition ...

The Kimura 3-parameter model is one of the most fundamental phylogenetic models in algebraic statistics. We prove that all varieties associated to this are projectively normal, confirming a conjecture Michałek.