P. Berglund and S. Katz: Nucl. Phys. B420 (1994) 289, hep-th/9311014.  Home/Search   Document Not in Database   Summary   Related Articles

....for which the weights admit a polynomial of Fermat type. Let w 1 ; w 5 be the elements of the dual lattice V (with r = 4) induced by the standard coordinate vectors of ZZ 5 . Recall that the fan for IP 4 k is the simplicial fan with edges spanned by w 1 ; w 5 . Since w i 2 r V[14], the edges of the cones of the fan of IP 4 k are a subset of the edges of the fan of Xr ; hence Xr is birational to IP 4 k ; it follows the the Calabi Yau hypersurfaces in Xr are birational to the original Calabi Yau hypersurfaces in IP 4 k . So Batyrev s construction is indeed an ....

....of toric geometry this corresponds to a finite quotient mapping[22] The process of refinement of F to get the subdivided normal fan corresponds to a birational transformation. In summary, the mirror family sits inside a partially desingularized orbifold of IP k r . We now recall from [14] that to the points e i of V correspond monomials in the toric variety determined by r, and one obtains a polynomial from adding up these terms. We can now observe that when referred back to IP k r as described above, this coincides with the transposed polynomial p. In other words, we must ....

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P. Berglund and S. Katz: Nucl. Phys. B420 (1994) 289, hep-th/9311014.

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