Equivalent Birational Embeddings III: cones

Two divisors in $\mathbb P^n$ are said to be Cremona equivalent if there is a Cremona modification sending one to the other. In this paper I study irreducible cones in $\mathbb P^n$ and prove that two cones are Cremona equivalent if their general hyperplane sections are birational. In particular I produce examples of cones in $\mathbb P^3$ Cremona equivalent to a plane whose plane section is not Cremona equivalent to a line in $\mathbb P^2$

Birational geometry of rational quartic surfaces

Two birational subvarieties of P^n are called Cremona equivalent if there is a Cremona modification of P^n mapping one to the other. If the codimension of the varieties is at least 2 then they are always Cremona Equivalent. For divisors the question is much more subtle and a general answer is unknown. In this paper I study the case of rational quartic surfaces and prove that they are all Cremona equivalent to a plane.Comment: Improved exposition after referee comments, 10 page

THE DRIVERS OF PRODUCTIVITY

This paper will try to demonstrate that productivity is the basis of all productive systems, which are viewed as transformers of utility and value, since the search for maximum productive efficiency is necessary to reduce production costs and thus produce value. After presenting a coherent frame of reference, we shall examine the drivers of productivity and then move on to discuss the consequences of the continual growth in productivity and the non-economic aspects linked to the gradual improvement in productivit