A conic bundle degenerating on the Kummer surface
| dc.creator | Bolognesi, Michele | |
| dc.date | 2007-02-18 | |
| dc.date.accessioned | 2026-07-07T07:47:33Z | |
| dc.date.available | 2026-07-07T07:47:33Z | |
| dc.description | Let $C$ be a genus 2 curve and $\su$ the moduli space of semi-stable rank 2 vector bundles on $C$ with trivial determinant. In \cite{bol:wed} we described the parameter space of non stable extension classes (invariant with respect to the hyperelliptic involution) of the canonical sheaf $ω$ of $C$ with $ω_C^{-1}$. In this paper we study the classifying rational map $ϕ: \pr Ext^1(ω,ω^{-1})\cong \pr^4 \dashrightarrow \su\cong \pr^3$ that sends an extension class on the corresponding rank two vector bundle. Moreover we prove that, if we blow up $\pr^4$ along a certain cubic surface $S$ and $\su$ at the point $p$ corresponding to the bundle $\OO \oplus \OO$, then the induced morphism $\tildeϕ: Bl_S \ra Bl_p\su$ defines a conic bundle that degenerates on the blow up (at $p$) of the Kummer surface naturally contained in $\su$. Furthermore we construct the $\pr^2$-bundle that contains the conic bundle and we discuss the stability and deformations of one of its components. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702525 | |
| dc.identifier | http://arxiv.org/abs/math/0702525 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124208 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60; 14J70 | |
| dc.title | A conic bundle degenerating on the Kummer surface | |
| dc.type | text |