Variation of the Brauer group and frequency of the Brauer-Manin obstruction for del Pezzo surfaces of degree four with a conic bundle structure

Vladimir Mitankin

It is well known that for a del Pezzo surface \(X\) of degree four over the rational numbers there are only three possibilities for the quotient of the Brauer group of \(X\) modulo constants. In this talk we will explain how often each of them appears when we range across a family of del Pezzo surfaces of degree four equipped with a conic bundle structure. We will also give an explicit description of the generators of this quotient which allows us to calculate the frequency of such surfaces with a Brauer-Manin obstruction to the existence of rational points. This talk is based on a joint work with Cecília Salgado.