Post #491

«Remarkably, many different flavors of mathematical objects can be classified by moduli spaces, and if the objects are algebro-geometric, the moduli space is usually an algebraic variety, often even a projective variety Surprising, right? (…) We are singularly focused on the question: Why do moduli spaces exist as varieties? By surveying how solutions to this question have evolved since Riemann’s work in the 1850s, we will reveal many of the central ideas in modern moduli theory, and we will do so using the language of stacks (…) While we present this material primarily in the algebraic setting, we also try to highlight parallel constructions in topology and analytic geometry» Jarod Alper. Evolution of Stacks and Moduli https://www.ams.org/journals/notices/202511/rnoti-p1248.pdf