Abstract
We construct in an abstract fashion (without using Gromov-Witten invariants) the orbifold quantum cohomology of weighted projective space, starting from a certain differential operator. We obtain the product, grading, and intersection form by making use of the associated self-adjoint D-module and the Birkhoff factorization procedure. The method extends inprinciple to the more difficult case of Fano hypersurfaces in weighted projective space, where Gromov-Witten invariants have not yet been computed, and we illustrate this by means of an example originally studied by A. Corti. In contrast to the case of weighted projective space itself or the case of a Fano hypersurface in projective space, a "small cell" of the Birkhoff decomposition plays a role in the calculation.
| Original language | English |
|---|---|
| Pages (from-to) | 273-297 |
| Number of pages | 25 |
| Journal | Commentarii Mathematici Helvetici |
| Volume | 89 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2014 |
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Keywords
- Birkhoff decomposition
- D-module
- Quantum cohomology
- Weighted projective space
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Orbifold quantum D-modules associated to weighted projective spaces. / Guest, Martin; Sakai, Hironori.
In: Commentarii Mathematici Helvetici, Vol. 89, No. 2, 2014, p. 273-297.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Orbifold quantum D-modules associated to weighted projective spaces
AU - Guest, Martin
AU - Sakai, Hironori
PY - 2014
Y1 - 2014
N2 - We construct in an abstract fashion (without using Gromov-Witten invariants) the orbifold quantum cohomology of weighted projective space, starting from a certain differential operator. We obtain the product, grading, and intersection form by making use of the associated self-adjoint D-module and the Birkhoff factorization procedure. The method extends inprinciple to the more difficult case of Fano hypersurfaces in weighted projective space, where Gromov-Witten invariants have not yet been computed, and we illustrate this by means of an example originally studied by A. Corti. In contrast to the case of weighted projective space itself or the case of a Fano hypersurface in projective space, a "small cell" of the Birkhoff decomposition plays a role in the calculation.
AB - We construct in an abstract fashion (without using Gromov-Witten invariants) the orbifold quantum cohomology of weighted projective space, starting from a certain differential operator. We obtain the product, grading, and intersection form by making use of the associated self-adjoint D-module and the Birkhoff factorization procedure. The method extends inprinciple to the more difficult case of Fano hypersurfaces in weighted projective space, where Gromov-Witten invariants have not yet been computed, and we illustrate this by means of an example originally studied by A. Corti. In contrast to the case of weighted projective space itself or the case of a Fano hypersurface in projective space, a "small cell" of the Birkhoff decomposition plays a role in the calculation.
KW - Birkhoff decomposition
KW - D-module
KW - Quantum cohomology
KW - Weighted projective space
UR - http://www.scopus.com/inward/record.url?scp=84903585182&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84903585182&partnerID=8YFLogxK
U2 - 10.4171/CMH/319
DO - 10.4171/CMH/319
M3 - Article
AN - SCOPUS:84903585182
VL - 89
SP - 273
EP - 297
JO - Commentarii Mathematici Helvetici
JF - Commentarii Mathematici Helvetici
SN - 0010-2571
IS - 2
ER -