On blowup of secant varieties of curves

Abstract

<p style='text-indent:20px;'>In this paper, we show that for a nonsingular projective curve and a positive integer <inline-formula><tex-math id="M1">\begin{document}$ k $\end{document}</tex-math></inline-formula>, the <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-th secant bundle is the blowup of the <inline-formula><tex-math id="M3">\begin{document}$ k $\end{document}</tex-math></inline-formula>-th secant variety along the <inline-formula><tex-math id="M4">\begin{document}$ (k-1) $\end{document}</tex-math></inline-formula>-th secant variety. This answers a question raised in the recent paper of the authors on secant varieties of curves.</p>