On the quantum cohomology of a symmetric product of an algebraic curve
| dc.creator | Bertram, Aaron | |
| dc.creator | Thaddeus, Michael | |
| dc.date | 1998-03-09 | |
| dc.date | 2001-01-23 | |
| dc.date.accessioned | 2026-07-07T05:24:01Z | |
| dc.date.available | 2026-07-07T05:24:01Z | |
| dc.description | The dth symmetric product of a curve of genus g is a smooth projective variety. This paper is concerned with the little quantum cohomology ring of this variety, that is, the ring having its 3-point Gromov-Witten invariants as structure constants. This is of considerable interest, for example as the base ring of the quantum category in Seiberg-Witten theory. The main results give an explicit, general formula for the quantum product in this ring unless d is in the narrow interval [3/4 g, g-1). Otherwise, they still give a formula modulo third order terms. Explicit generators and relations are also given unless d is in [4/5 g - 3/5, g-1). The virtual class on the space of stable maps plays a significant role. But the central ideas ultimately come from Brill-Noether theory: specifically a formula of Harris-Tu for the Chern numbers of determinantal varieties. The case d = g-1 is especially interesting: it resembles that of a Calabi-Yau 3-fold, and the Aspinwall-Morrison formula enters the calculations. A detailed analogy with Givental's work is also explained. | |
| dc.description | 28 pages; LaTeX2e, with packages amsfonts, latexsym, eepic | |
| dc.identifier | https://arxiv.org/abs/math/9803026 | |
| dc.identifier | http://arxiv.org/abs/math/9803026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76676 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 14H99 | |
| dc.title | On the quantum cohomology of a symmetric product of an algebraic curve | |
| dc.type | text |