Stable vector bundles on fibered threefolds over a surface

期刊论文
发表日期：

2024年9月9日

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Tohru Nakashima

摘要

Let X be a smooth projective threefold and let H be an ample line bundle on X. We investigate the existence of vector bundles on X which are $\mu $ $μ$ -stable with respect to an ample divisor $H_{\epsilon }=H+\epsilon D$ $H_{ϵ} = H + ϵ D$ for sufficiiently small $\epsilon >0$ $ϵ > 0$ where D is a divisor with $D\cdot H^2=0$ $D \cdot H^{2} = 0$ . In particular, when X is a Fano conic bundle over a rational surface, we show that there exists a family $\{E_n\}$ ${E_{n}}$ of $H_{\epsilon }$ $H_{ϵ}$ -stable vector bundles with $c_1(E_n)=0$ $c_{1} (E_{n}) = 0$ and $c_2(E_n)\cdot H$ $c_{2} (E_{n}) \cdot H$ becomes arbitrarily large as n goes to infinity.