$O(-2)$ Blow-up Formula via Instanton Calculus on $\hat{C^2/Z_2}$ and Weil Conjecture
| dc.creator | Sasaki, Toru | |
| dc.date | 2006-03-21 | |
| dc.date | 2006-05-16 | |
| dc.date.accessioned | 2026-07-07T07:06:16Z | |
| dc.date.available | 2026-07-07T07:06:16Z | |
| dc.description | We calculate Betti numbers of the framed moduli space of instantons on $\hat{{\bf C}^2/{\bf Z}_2}$, under the assumption that the corresponding torsion free sheaves $E$ have vanishing properties ($Hom(E,E(-l_\infty))=Ext^2(E,E(-l_\infty))=0$). Moreover we derive the generating function of Betti numbers and obtain closed formulas. On the other hand, we derive a universal relation between the generating function of Betti numbers of the moduli spaces of stable sheaves on $X$ with an $A_1$-singularity and that on $\hat{X}$ blow-uped at the singularity, by using Weil conjecture. We call this the $O(-2)$ blow-up formula. Applying this to $X={\bf C}^2/{\bf Z}_2$ case, we reproduce the formula given by instanton calculus. | |
| dc.description | 31 pages, reference and appendix added | |
| dc.identifier | https://arxiv.org/abs/hep-th/0603162 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0603162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109961 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | $O(-2)$ Blow-up Formula via Instanton Calculus on $\hat{C^2/Z_2}$ and Weil Conjecture | |
| dc.type | text |