Caltech/USC Joint Algebra and Geometry Seminar (2/2)

In the study of derived categories of coherent sheaves, ample line bundles play a fundamental role: their tensor powers generate the derived category. We call a line bundle with this property tensor-generating. For toric varieties, tensor-generation admits a purely combinatorial criterion, and there exist many tensor-generating line bundles that are neither ample nor anti-ample, including examples on complete non-projective toric varieties. In this talk, I will further explore the relationship between tensor-generation and nonstandard autoequivalences of the derived category. This is joint work in progress with Michael Zeng and Xiangru Zeng.