P. Berglund and S. Katz: Mirror Symmetry Constructions: A review, IASSNSHEP -94/38, OSU-M-94-2, to appear in "Essays on Mirror Manifolds, II", hepth /9406008.  Home/Search   Document Not in Database   Summary   Related Articles

....point would have to have 0 x 4 1, which is impossible) The origin now lies in the facet f 5 . 3. A Generalized Transposition Rule 3.1. Generalization of the Berglund Hubsch rule In this section we generalize the transposition rule of Berglund and Hubsch[19] For a review and examples see [20]. Suppose that, as previously, one starts with a weighted projective space IP k r whose Newton polyhedron Delta is reflexive. Suppose that one is also given r 1 monomials m 1 ; m r 1 of degree d. Let a i = m i Gamma 1, so that a i 2 . Suppose in addition that the a i span IR . ....

....basis vector corresponding to the variable (the one for which the position of the 1 is determined by the subscript of the variable) This immediately gives the desired result. More precisely, we obtain the columns of A T by this procedure, then add 1 to get M T . Examples appear in [20]. The final thing to do is to verify that the group of geometric symmetries has the claimed order. Of course, the toric method gives the group explicitly, so we have given more information than noticed by Berglund and Hubsch (but see [23] To do this, we must show that mirror symmetry exchanges ....

P. Berglund and S. Katz: Mirror Symmetry Constructions: A review, IASSNSHEP -94/38, OSU-M-94-2, to appear in "Essays on Mirror Manifolds, II", hepth /9406008.

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