Geometry & Geometric Analysis Seminar
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and other campuses to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
Next talks: *Monday*, November 2 and 9, 4 pm, TUC 352
Speaker: Zhaoting Wei (East Texas A&M University)
In 2011, Khalkhali, Landi, and Van Suijlekom introduced the quantum projective line as a noncommutative complex manifold and constructed the standard holomorphic structures on line bundles over it. They posed the question of whether every holomorphic structure on such line bundles is gauge equivalent to the standard ones. In this talk, we give a negative answer to this question. In fact, we show that there exist at least countably many distinct gauge equivalence classes of holomorphic structures on these line bundles—a phenomenon in stark contrast to the commutative case. This is a joint work with Graveman, La Rue, MacArthur, and Pesin.
I will first give the background of noncommutative complex geometry and the construction of quantum projective spaces, then move on to the construction of non-standard holomorphic line bundles.