Carrell and Peterson proved a test for rational smoothness of Schubert varieties at torus-fixed points, which depends on the number of torus-fixed curves through such points. The lookup conjecture of Boe and Graham is a conjectural simplification of the Carrell-Peterson criterion for rational smoothness. In this talk I will survey previous work by Boe-Graham and Graham-Li on the lookup conjecture, and describe recent work with Brian Boe. We identify the locus of rationally smooth points of a Schubert variety of type Ã2, and complete the proof of the lookup conjecture of Boe and Graham in type Ã2. We also identify the locus of smooth points (which is different from the rationally smooth locus).
This talk is based on joint work with Brian Boe.
This video is part of the University of Georgia‘s Algebra seminar.
