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Algebraic Geometry Seminar
Seminar information archive ～01/03｜Next seminar｜Future seminars 01/04～
| Date, time & place | Friday 13:30 - 15:00 118Room #118 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, KAWAKAMI Tatsuro, ENOKIZONO Makoto |
2025/12/19
15:15-16:45 Room #118 (Graduate School of Math. Sci. Bldg.)
JongHae Keum (Korea Institute for Advanced Study)
Fake quadric surfaces
JongHae Keum (Korea Institute for Advanced Study)
Fake quadric surfaces
[ Abstract ]
A smooth projective complex surface S is called a Q-homology quadric if it has the same Betti numbers as the smooth quadric surface.
Let S be a Q-homology quadric. Then its cohomology lattice is of rank 2, (even or odd) unimodular.
By the classification theory of surfaces, S is either rational or of general type.
In the latter case, S is called a fake Q-homology quadric.
There is an unsolved question raised by Hirzebruch: does there exist a surface of general type which is homeomorphic to the smooth quadric surface?
I will report recent progress on these surfaces.
A smooth projective complex surface S is called a Q-homology quadric if it has the same Betti numbers as the smooth quadric surface.
Let S be a Q-homology quadric. Then its cohomology lattice is of rank 2, (even or odd) unimodular.
By the classification theory of surfaces, S is either rational or of general type.
In the latter case, S is called a fake Q-homology quadric.
There is an unsolved question raised by Hirzebruch: does there exist a surface of general type which is homeomorphic to the smooth quadric surface?
I will report recent progress on these surfaces.
