This article is cited in 7 papers

Stable bundles with $c_1=0$ on rational surfaces

I. V. Artamkin


Abstract: For an arbitrary rational surface $X$the author proves the existence of a nonempty component of the moduli variety $M^0(X,n,r)$ of rank $r$ bundles with $c_1=0$ and $c_2=n\geqslant r$ in which the $\mathscr L$-stable bundles constitute a nonempty open subset for any ample $\mathscr L$. Moreover, any birational isomorphism $\varphi\colon X\to Y$ of surfaces gives rise to a birational isomorphism $\varphi_*\colon M^0(X)\to M^0(Y)$.

UDC: 512.7

MSC: Primary 14J25, 14F05; Secondary 14E05

Received: 22.11.1988

 English version: Mathematics of the USSR-Izvestiya, 1991, 36:2, 231–246

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