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Fano Varieties and Extremal Laurent Polynomials

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Visit this site: http://coates.ma.ic.ac.uk/fanosearch/

Author:Coates, Tom; Corti, Alessio; Galkin, Sergey; Golyshev, Vasily; Kasprzyk, Al
Description: 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 five-dimensional shapes. Along the way, see pictures of the anticanonical surfaces inside Fano 3-folds, 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 3-folds; computing the quantum cohomology connection matrices for each of the Fano 3-folds on the Mori–Mukai list; finding Minkowksi polynomials corresponding to each of the 3-folds; and testing the speculative conjecture that a reflexive 3-dimensional 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: Web-Based Discussions, Internet-Based Projects
Math Topics: Higher-Dimensional Geometry

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