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A Mirror Theorem for T-Equivariant Blowups

2015/10/05 by Jeff Brown, Brown, Jeff
Mathematics · #14-02 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14-02

paper · pdf · doi:10.48550/arxiv.1510.01301

55 pages

arxiv created 2015/10/05 · arxiv updated 2015/10/06

Abstract

Let E be a toric fibration arising from symplectic reduction of a direct sum of line bundles over (almost-) Kähler base B. Then each torus-fixed point of the toric manifold fiber defines a section of the fibration. Let La be convex line bundles over B, Aa smooth divisors of B arising as the zero loci of generic sections of La, and \a:B→ E a particular fixed-point section of E. Further assume the \Aa\ to be mutually disjoint. We compute genus-0 Gromov--Witten invariants of the blowup of E along \a(\coproda Aa) in terms of genus-0 Gromov--Witten invariants of B and of \Aa\, the matrix used for the symplectic reduction description of the fiber of the toric fibration E→ B, and the restriction maps iAa^*:H^*(B)→ H^*(Aa).

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