Mirror symmetry and projective geometry of Reye congruences I

By S. Hosono, Hiromichi Takagi. 2011

49 citations recorded by the source corpus.

Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mP^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mP^4$ branched over a curve. We also calculate BPS numbers of both $X$ and $Y$ (and also a related Calabi-Yau complete intersection $\tilde X_0$) using mirror symmetry.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/621dd2a3be5ab42786c6b7d0af6be3c44f277e70

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Two-Sphere Partition Functions and Gromov–Witten Invariants (2012, background): “14 Other examples of this phenomenon can be seen in [10,83].”
Variation of geometric invariant theory quotients and derived categories (2012, background): “r,s,t) to get some nice statements. If r= s= t= n, then Vxy,Vxu,Vyu are all derived equivalent Calabi-Yau varieties. For generic choices of Qu 0,...,Q u r, they are not isomorphic but are birational, [HT11]. If r= s+t, then generically Qu 0,...,Q u r intersect only at the origin. Thus, Db(cohV xy) i”
Duality in two-dimensional (2,2) supersymmetric non-Abelian gauge theories (2011, methodology): “X̃S and XS are three dimensional Calabi-Yau manifolds, with h (1,1)(X̃S) = 2, h (2,1)(X̃S) = 52 and h(1,1)(XS) = 1, h (2,1)(XS) = 26 [15].”