Geometric section conjecture for the boundary divisor D2D_2

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Let A∗(M‾0,2(P1,2))A^*({\overline{\mathcal{M}}}_{0,2}({\mathbb P}^1,2)) denote the Chow ring of the moduli space of stable maps, let L1L_1 and L2L_2 be the cotangent line bundles associated with the two marked points, and let D2D_2 be the boundary divisor. Geometric section conjecture. There exists a section ss of the line bundle L1\*L2L_1\* L_2 on A∗(M‾0,2(P1,2))A^*({\overline{\mathcal{M}}}_{0,2}({\mathbb P}^1,2)) whose zero stack is the boundary divisor D2D_2. The proposed section would give a geometric explanation for the relation D2−ψ1−ψ2D_2-\psi_1-\psi_2 and replace the paper's localization and linear-algebra argument; the source does not establish its existence.

References

Primary source

Jonathan A. Cox, “A presentation for the Chow ring of M_0,2(P^1,2)”, arXiv:math/0504575 (2005).

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