Seminar

Question: for A in SL(4), when does CC^4/A have a crepant resolution? If you expect Calabi-Yau 4-fold geometry to be analogous to the 3-fold case you are probably in for a disappointment. Even in cases when a crepant resolution exists, A-Hilb CC^4 may be bad, for example containing exuberant components. In the longer term, this may be a test case for derived geometry. I will give some algorithms and examples, and suggest some questions on relations between A-Hilb CC^4 computed in toric geometry and Hilb^n CC^3. This is speculative material, so don't expect any of it to be correct. For related material, see our website

www.warwick.ac.uk/staff/T.Logvinenko/Traps