A theory of the invariants obtained from the moduli stacks of stable objects on a smooth polarized surface
| dc.creator | Mochizuki, Takuro | |
| dc.date | 2002-10-15 | |
| dc.date | 2006-07-07 | |
| dc.date.accessioned | 2026-07-07T06:35:31Z | |
| dc.date.available | 2026-07-07T06:35:31Z | |
| dc.description | Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental classes of some moduli stacks, and we show the transition formula of the integrals over the moduli stacks of the $δ$-stable Bradlow pairs for the variation of the parameter $δ$. Then, we study the relation among the invariants. In the case $p_g>0$, we show that the invariants are independent of the choice of a polarization of $X$. We also show that the invariants can be reduced to the invariants obtained from the moduli of abelian pairs and the Hilbert schemes. In the case $p_g=0$, we obtain the weak wall crossing formula and the weak intersection rounding formula, which describes the dependence of the invariants on the polarization. | |
| dc.description | The transition formula is obtained in the higher rank case. The manuscript is completely revised | |
| dc.identifier | https://arxiv.org/abs/math/0210211 | |
| dc.identifier | http://arxiv.org/abs/math/0210211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99818 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D20, 14J60, 14J80 | |
| dc.title | A theory of the invariants obtained from the moduli stacks of stable objects on a smooth polarized surface | |
| dc.type | text |