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Full-Text Articles in Algebraic Geometry
A Constructive Proof Of Ky Fan's Generalization Of Tucker's Lemma, Timothy Prescott '02, Francis E. Su
A Constructive Proof Of Ky Fan's Generalization Of Tucker's Lemma, Timothy Prescott '02, Francis E. Su
All HMC Faculty Publications and Research
We present a proof of Ky Fan's combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan's lemma to allow for triangulations of Sn that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker's lemma that holds for a more general class of triangulations than the usual version.
The Closed Topological Vertex Via The Cremona Transform, Jim Bryan, Dagan Karp
The Closed Topological Vertex Via The Cremona Transform, Jim Bryan, Dagan Karp
All HMC Faculty Publications and Research
We compute the local Gromov-Witten invariants of the "closed vertex", that is, a configuration of three rational curves meeting in a single triple point in a Calabi-Yau threefold. The method is to express the local invariants of the vertex in terms of ordinary Gromov-Witten invariants of a certain blowup of CP^3 and then to compute those invariants via the geometry of the Cremona transformation.