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Algebraic Geometry Seminar
Seminar information archive ～05/02｜Next seminar｜Future seminars 05/03～
| Date, time & place | Friday 13:30 - 15:00 118Room #118 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, KAWAKAMI Tatsuro, ENOKIZONO Makoto |
2014/05/12
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Andrés Daniel Duarte (Institut de Mathématiques de Toulouse)
Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem (ENGLISH)
Andrés Daniel Duarte (Institut de Mathématiques de Toulouse)
Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem (ENGLISH)
[ Abstract ]
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.
