We shall proceed to the study of threefold Mori fibre spaces. This chapter is an introduction to the Sarkisov program, which factorises a birational map of Mori fibre spaces as a composite of elementary maps called Sarkisov links. Corti established it in dimension three. The program twists the birational map into an isomorphism by means of the Noether-Fano inequality. Whereas Hacon and McKernan obtained a new program in an arbitrary dimension, we stick to the traditional approach which fits better into the explicit study. The program stems from the pioneer work of Iskovskikh and Manin on the irrationality of a smooth quartic threefold. We review the rationality problem and discuss the notions of rationality, stable rationality and unirationality. A rational variety has a large number of Mori fibre spaces in its birational class. Oppositely, a variety birational to essentially only one Mori fibre space is said to be birationally rigid. We explain a general strategy for applying the Sarkisov program to the rationality and birational rigidity problem, and demonstrate this by an example due to Corti and Mella which has exactly two birational structures of a Mori fibre space.

“From the outside, the market in India is often seen as an exchange arena bound by state-imposed rules. Those within - buyers and sellers, producers and consumers, brokers and advertisers, financiers and debtors, police and inspectors - understand it differently. Such parties collude and compete in myriad everyday activities. These include those of accumulation and circulation, of production and speculation, and of arbitrage and management.

Involved actors, in short, experience the Indian market dissimilarly from the ways in which many planners and policymakers comprehend it. This market is best understood as an ensemble of practices and institutions. It has active and reactive patterns of economic and sociocultural practices, flexible adjustment and coping mechanisms, unforeseen contingencies and aberrations, and strategies of ambiguity and transgression. Transactional agents navigate gray areas and tacit understandings. They reproduce durable informal relations and customary practices. These dynamics only partially relate to state-led market-framing processes.”