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Algebraic Geometry Seminar
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
| Date, time & place | Friday 13:30 - 15:00 ハイブリッド開催/117Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, NAKAMURA Yusuke, TANAKA Hiromu |
2019/06/19
15:30-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Fumiaki Suzuki (UIC)
A pencil of Enriques surfaces with non-algebraic integral Hodge classes (TBA)
Fumiaki Suzuki (UIC)
A pencil of Enriques surfaces with non-algebraic integral Hodge classes (TBA)
[ Abstract ]
The integral Hodge conjecture is the statement that the integral Hodge classes are algebraic on smooth complex projective varieties. It is known that the conjecture can fail in general. There are two types of counterexamples, ones with non-algebraic integral Hodge classes of torsion-type and of non-torsion type, the first of which were given by Atiyah-Hirzebruch and Kollar, respectively.
In this talk, we exhibit a pencil of Enriques surfaces defined over Q with non-algebraic integral Hodge classes of non-torsion type. This construction relates to certain questions concerning rational points of algebraic varieties.
This gives the first example of a threefold with the trivial Chow group of zero-cycles on which the integral Hodge conjecture fails. As an application, we construct a fourfold which gives the negative answer to a classical question on the universality of the Abel-Jacobi maps.
This is a joint work with John Christian Ottem.
The integral Hodge conjecture is the statement that the integral Hodge classes are algebraic on smooth complex projective varieties. It is known that the conjecture can fail in general. There are two types of counterexamples, ones with non-algebraic integral Hodge classes of torsion-type and of non-torsion type, the first of which were given by Atiyah-Hirzebruch and Kollar, respectively.
In this talk, we exhibit a pencil of Enriques surfaces defined over Q with non-algebraic integral Hodge classes of non-torsion type. This construction relates to certain questions concerning rational points of algebraic varieties.
This gives the first example of a threefold with the trivial Chow group of zero-cycles on which the integral Hodge conjecture fails. As an application, we construct a fourfold which gives the negative answer to a classical question on the universality of the Abel-Jacobi maps.
This is a joint work with John Christian Ottem.
