Rational Curves in Rigid Calabi-Yau Three-folds
| dc.creator | Roan, Shi-shyr | |
| dc.date | 2003-12-21 | |
| dc.date.accessioned | 2026-07-07T05:04:06Z | |
| dc.date.available | 2026-07-07T05:04:06Z | |
| dc.description | We determine all the Kummer-surface-type Calabi-Yau (CY) 3-folds, i.e., those $\hat{T/G}$ which are resolutions of 3-torus-orbifolds $T/G$ with only isolated singularities. There are only two such CY spaces: one with $G= \ZZ_3$ and $T$ being the triple-product of 1-torus carrying an order 3 automorphism, the other with $G= \ZZ_7$ and $T$ being the Jacobian of Klein quartic curve. These CY 3-folds $\hat{T/G}$ are all rigid, hence no complex structure deformation for each of these two varieties. We further investigate problems of $\PZ^1$-curves $C$ in $\hat{T/G}$ not contained in exceptional divisors, by considering the counting number $d$ of elements in $C$ meeting exceptional divisors in a certain manner. We have obtained the constraint of $d$. With the smallest number $d$, the complete solution of $C$ in $\hat{T/G}$ is obtained for both cases. In the case $G=\ZZ_3$, we have derived an effective method of constructing $C$ in $\hat{T/G}$, and obtained the explicit forms of rational curves for some other $d$ by this procedure. | |
| dc.description | LaTeX 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312399 | |
| dc.identifier | http://arxiv.org/abs/math/0312399 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69672 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 11G, 14E, 14J, 14K | |
| dc.title | Rational Curves in Rigid Calabi-Yau Three-folds | |
| dc.type | text |