Global Okounkov bodies for Bott-Samelson varieties

We use the theory of Mori dream spaces to prove that the global Okounkov body of a Bott-Samelson variety with respect to a natural flag of subvarieties is rational polyhedral. In fact, we prove more generally that this holds for any Mori dream space which admits a flag of Mori dream spaces satisfying a certain regularity condition. As a corollary, Okounkov bodies of effective line bundles over Schubert varieties are shown to be rational polyhedral. In particular, it follows that the global Okounkov body of a flag variety $G/B$ is rational polyhedral. As an application we show that the asymptotic behaviour of dimensions of weight spaces in section spaces of line bundles is given by the counting of lattice points in polytopes.Comment: A new and simpler definition of a good flag is introduced, and Bott-Samelson varieties are shown to admit such flag

Newton-Okounkov bodies and complexity functions

We show that quite universally the holonomicity of the complexity function of a big divisor on a projective variety does not predict the polyhedrality of the Newton-Okounkov body associated to every flag

Pancreatitis in pregnancy

This issue of eMedRef provides information to clinicians on the pathophysiology, diagnosis, and therapeutics of pancreatitis in pregnancy