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Algebraic Geometry Seminar
Seminar information archive ～05/21｜Next seminar｜Future seminars 05/22～
| Date, time & place | Friday 13:30 - 15:00 118Room #118 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, KAWAKAMI Tatsuro, ENOKIZONO Makoto |
2017/05/09
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Kohsuke Shibata (The University of Tokyo)
Upper bound of the multiplicity of locally complete intersection singularities (English)
Kohsuke Shibata (The University of Tokyo)
Upper bound of the multiplicity of locally complete intersection singularities (English)
[ Abstract ]
The multiplicity of a point on a variety is a fundamental invariant to estimate how the singularity is bad. It is introduced in a purely algebraic context. On the other hand, we can also attach to the singularity the log canonical threshold and the minimal log discrepancy, which are introduced in a birational theoretic context. In this talk, we show bounds of the multiplicity by functions of these birational invariants for a singularity of locally a complete intersection. As an application, we obtain the affirmative answer to Watanabe’s conjecture on the multiplicity of canonical singularity of locally a complete intersection up to dimension 32.
The multiplicity of a point on a variety is a fundamental invariant to estimate how the singularity is bad. It is introduced in a purely algebraic context. On the other hand, we can also attach to the singularity the log canonical threshold and the minimal log discrepancy, which are introduced in a birational theoretic context. In this talk, we show bounds of the multiplicity by functions of these birational invariants for a singularity of locally a complete intersection. As an application, we obtain the affirmative answer to Watanabe’s conjecture on the multiplicity of canonical singularity of locally a complete intersection up to dimension 32.
