Unchaining surgery, branched covers, and pencils on elliptic surfaces
Geometric Topology
2023-09-13 v1 Symplectic Geometry
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.
Cite
@article{arxiv.2108.04868,
title = {Unchaining surgery, branched covers, and pencils on elliptic surfaces},
author = {Terry Fuller},
journal= {arXiv preprint arXiv:2108.04868},
year = {2023}
}
Comments
24 pages, 32 figures