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Geometric Analysis Seminar
Seminar information archive ～07/28｜Next seminar｜Future seminars 07/29～
| Organizer(s) | Shouhei Honda, Hokuto Konno, Asuka Takatsu |
|---|---|
| URL | https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/ |
2025/07/10
14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Jeff Viaclovsky (University of California, Irvine)
Fibrations on the $6$-sphere and Clemens threefolds (英語)
Jeff Viaclovsky (University of California, Irvine)
Fibrations on the $6$-sphere and Clemens threefolds (英語)
[ Abstract ]
Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from $Z$ onto any $2$-dimensional complex space. In other words, $Z$ can only possibly fiber over a curve. This result applies in particular to a class of threefolds, known as Clemens threefolds, which are diffeomorphic to a connected sum of $k$ copies of $S^3 \times S^3$ for $k > 1$. This result also gives a new restriction on any hypothetical complex structure on the $6$-sphere $S^6$. This is joint work with Nobuhiro Honda.
Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from $Z$ onto any $2$-dimensional complex space. In other words, $Z$ can only possibly fiber over a curve. This result applies in particular to a class of threefolds, known as Clemens threefolds, which are diffeomorphic to a connected sum of $k$ copies of $S^3 \times S^3$ for $k > 1$. This result also gives a new restriction on any hypothetical complex structure on the $6$-sphere $S^6$. This is joint work with Nobuhiro Honda.
