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Explore explicit constructions of K-moduli spaces for Fano 3-folds and their connections to other modular frameworks in this mathematical lecture. Delve into specific examples that illustrate the geometric properties and modular behavior of these important algebraic varieties. Examine how K-moduli spaces relate to alternative modular constructions, providing insight into the broader landscape of moduli theory in algebraic geometry. Learn about the technical aspects of constructing these moduli spaces explicitly, with particular focus on three-dimensional Fano varieties and their deformation theory. Gain understanding of the interplay between K-stability, moduli problems, and birational geometry through concrete examples and detailed mathematical analysis presented during this specialized research talk from the Jean Morlet Chair thematic meeting on real algebraic geometry and birational geometry.
