Noncommutative algebras and (commutative) algebraic geometry


Morrison, D. (2010). Noncommutative algebras and (commutative) algebraic geometry. Perimeter Institute. https://pirsa.org/10050040


Morrison, David. Noncommutative algebras and (commutative) algebraic geometry. Perimeter Institute, May. 08, 2010, https://pirsa.org/10050040


          @misc{ pirsa_PIRSA:10050040,
            doi = {10.48660/10050040},
            url = {https://pirsa.org/10050040},
            author = {Morrison, David},
            keywords = {},
            language = {en},
            title = {Noncommutative algebras and (commutative) algebraic geometry},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050040 see, \url{https://pirsa.org}}

David Morrison University of California, Santa Barbara


The study of D-branes at singular points of Calabi-Yau threefolds has revealed interesting connections between certain noncommutative algebras and singular algebraic varieties. In many respects, the choice of an appropriate noncommutative algebra is analogous to finding a resolution of singularities of the variety. We will explain this connection in detail, and outline a program for studying such ''noncommutative resolutions'' globally, for compact algebraic (Calabi--Yau) threefolds.