Infinitely many Lefschetz pencils on ruled surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917264742154240 |
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| author | Lee, Seraphina Eun Bi Serván, Carlos A. |
| author_facet | Lee, Seraphina Eun Bi Serván, Carlos A. |
| contents | We show that any ruled surface $X$ with $χ(X) < 0$ admits infinitely many inequivalent Lefschetz pencils of fixed genus and number of base points. Our proof proceeds by building infinitely many inequivalent Lefschetz fibrations on a blow-up $X \# 4 \overline{\mathbb{CP}^2}$ of $X$ with constant fiber class, via a mechanism known as partial conjugation. Furthermore, there exists a symplectic form on $X$ compatible with all such pencils, and similarly for the fibrations in $X\#4\overline{\mathbb{CP}^2}$. This provides the first example of this phenomenon and makes progress on Problem 4.98 of the K3 list of problems in low-dimensional topology in the case of ruled surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Infinitely many Lefschetz pencils on ruled surfaces Lee, Seraphina Eun Bi Serván, Carlos A. Geometric Topology Symplectic Geometry We show that any ruled surface $X$ with $χ(X) < 0$ admits infinitely many inequivalent Lefschetz pencils of fixed genus and number of base points. Our proof proceeds by building infinitely many inequivalent Lefschetz fibrations on a blow-up $X \# 4 \overline{\mathbb{CP}^2}$ of $X$ with constant fiber class, via a mechanism known as partial conjugation. Furthermore, there exists a symplectic form on $X$ compatible with all such pencils, and similarly for the fibrations in $X\#4\overline{\mathbb{CP}^2}$. This provides the first example of this phenomenon and makes progress on Problem 4.98 of the K3 list of problems in low-dimensional topology in the case of ruled surfaces. |
| title | Infinitely many Lefschetz pencils on ruled surfaces |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2602.10051 |