Fano Varieties and Extremal Laurent Polynomials
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http://coates.ma.ic.ac.uk/fanosearch/  


Coates, Tom; Corti, Alessio; Galkin, Sergey; Golyshev, Vasily; Kasprzyk, Al  
This research collaboration blogs about the creation of a directory of all possible shapes and geometric building blocks in the universe  the equivalent of a periodic table of the elements for three, four, and fivedimensional shapes. Along the way, see pictures of the anticanonical surfaces inside Fano 3folds, the "elements" in the team's "periodic table of shapes." "To do's" include computing Picard–Fuchs operators; identifying the remaining two D3 forms in the list of Minkowski D3 forms; proving Galkin's statements about the Fano 3folds; computing the quantum cohomology connection matrices for each of the Fano 3folds on the Mori–Mukai list; finding Minkowksi polynomials corresponding to each of the 3folds; and testing the speculative conjecture that a reflexive 3dimensional polytope P admits a Minkowksi polynomial if and only if the toric variety corresponding to P can be smoothed.  


Levels:  Research 
Languages:  English 
Resource Types:  WebBased Discussions, InternetBased Projects 
Math Topics:  HigherDimensional Geometry 
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