In a joint project with Vladimiro Benedetti, Sara Angela Filippini, and Laurent Manivel, we introduce a new class of varieties, called orbital degeneracy loci. They are modelled on any orbit closure in a representation of an algebraic group and generalize classical degeneracy loci of morphisms between vector bundles or zero loci of sections. In this talk I will introduce some tools to understand and study this new class of objects; with such techniques, we can exploit our construction to produce several interesting examples of projective varieties, in particular varieties with trivial or negative canonical bundle. |

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