Bondal-Polishchuk’s conjecture for Fano threefolds of Picard rank one

Anya Nordskova (University of Hasselt)

Tuesday 25th February 15:00-16:00 Maths 311B

Abstract

In 1993, Bondal and Polishchuk conjectured that the braid group action on the set of full exceptional collections in a triangulated category is always transitive. In this general form the conjecture has been disproved just recently by Chang, Haiden and Schroll. However, if one restricts to derived categories of smooth projective varieties, the question is still widely open. I will sketch the proof of Bondal-Polishchuk’s conjecture for threefolds admitting a full exceptional collection of length 4 (in particular, the projective space P^3). This is the first 3-dimensional case where the transitivity has been verified. Our proof employs a detailed analysis of the group generated by spherical twists on an anticanonical divisor, which we believe to be of independent interest. The talk is based on joint work with Michel Van den Bergh. 

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