Unchaining surgery, branched covers, and pencils on elliptic surfaces

Terry Fuller

doi:10.2140/agt.2023.23.2867

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arXiv · 2108.04868

Unchaining surgery, branched covers, and pencils on elliptic surfaces

Terry Fuller

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Abstract

We show that every member of an infinite family of symplectic manifolds constructed by R. Inanc Baykur, Kenta Hayano, and Naoyuki Monden (arXiv:1903:02906) is diffeomorphic to an elliptic surface. As a result: (1) the symplectic Calabi-Yau 4-manifolds among their family are diffeomorphic to the standard K3 surface; (2) each elliptic surface E(n) admits a genus g Lefschetz pencil, for all g greater than or equal to n; and (3) each elliptic surface E(n) blown up once admits a pair of inequivalent genus g Lefschetz pencils, for all g greater than or equal to n.

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Terry Fuller. 2021-08-10. Unchaining surgery, branched covers, and pencils on elliptic surfaces. https://doi.org/10.2140/agt.2023.23.2867

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