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Algebraic Geometry Seminar
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Friday 13:30 - 15:00 118Room #118 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, KAWAKAMI Tatsuro, ENOKIZONO Makoto |
2011/01/31
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Sukmoon Huh (KIAS)
Restriction maps to the Coble quartic (ENGLISH)
Sukmoon Huh (KIAS)
Restriction maps to the Coble quartic (ENGLISH)
[ Abstract ]
The Coble sixfold quartic is the moduli space of semi-stable vector bundle of rank 2 on a non-hyperelliptic curve of genus 3 with canonical determinant. Considering the curve as a plane quartic, we investigate the restriction of the semi-stable sheaves over the projective plane to the curve. We suggest a positive side of this trick in the study of the moduli space of vector bundles over curves by showing several examples such as Brill-Noether loci and a few rational subvarieties of the Coble quartic. In a later part of the talk, we introduce the rationality problem of the Coble quartic. If the time permits, we will apply the same idea to the moduli space of bundles over curves of genus 4 to derive some geometric properties of the Brill-Noether loci in the case of genus 4.
The Coble sixfold quartic is the moduli space of semi-stable vector bundle of rank 2 on a non-hyperelliptic curve of genus 3 with canonical determinant. Considering the curve as a plane quartic, we investigate the restriction of the semi-stable sheaves over the projective plane to the curve. We suggest a positive side of this trick in the study of the moduli space of vector bundles over curves by showing several examples such as Brill-Noether loci and a few rational subvarieties of the Coble quartic. In a later part of the talk, we introduce the rationality problem of the Coble quartic. If the time permits, we will apply the same idea to the moduli space of bundles over curves of genus 4 to derive some geometric properties of the Brill-Noether loci in the case of genus 4.
