Bounded derived categories of coherent sheaves play a crucial role in the study of the geometry of projective varieties. Their semiorthogonal decompositions build connections to other varieties and reflect many properties such as singularity and rationality. I will talk about the motivation to study these structures, illustrate the important examples of Bondal-Orlov and Burban, and report on my work about smooth complete intersections of three quadrics and nodal quintic del Pezzo threefolds that generalize their examples.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/158