AI 中文总结
该研究确定了广义Bott-Samelson流形的格罗莫夫宽度由其极小有理曲线的辛面积给出，并据此得到这类流形关于丰富线丛的塞萨德里常数的上界。
AI 中文摘要
我们研究光滑广义Bott-Samelson簇的格罗莫夫宽度，这类射影簇由Perrin在文献\uc16b{Per07}中构造，是经典Bott-Samelson消解的舒伯特簇的推广。我们证明，配备有理凯勒形式的此类簇的格罗莫夫宽度，由其极小有理曲线的辛面积给出。由此，我们得到这类簇关于丰富线丛的塞萨德里常数的上界。
英文摘要
We study the Gromov width of smooth generalized Bott-Samelson varieties, a class of projective varieties constructed by Perrin in \cite{Per07} as a generalization of classical Bott-Samelson resolutions of Schubert varieties. We show that the Gromov width of such a variety equipped with a rational Kähler form is given by the symplectic area of its minimal rational curves. As a consequence, we obtain upper bounds for the Seshadri constants of these varieties with respect to ample line bundles.
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