### Electronic Research Archive

2021, Issue 6: 3649-3654. doi: 10.3934/era.2021055
Special Issues

# On blowup of secant varieties of curves

• Received: 01 March 2021 Published: 22 July 2021
• 14N07, 14C05

• In this paper, we show that for a nonsingular projective curve and a positive integer $k$, the $k$-th secant bundle is the blowup of the $k$-th secant variety along the $(k-1)$-th secant variety. This answers a question raised in the recent paper of the authors on secant varieties of curves.

Citation: Lawrence Ein, Wenbo Niu, Jinhyung Park. On blowup of secant varieties of curves[J]. Electronic Research Archive, 2021, 29(6): 3649-3654. doi: 10.3934/era.2021055

### Related Papers:

• In this paper, we show that for a nonsingular projective curve and a positive integer $k$, the $k$-th secant bundle is the blowup of the $k$-th secant variety along the $(k-1)$-th secant variety. This answers a question raised in the recent paper of the authors on secant varieties of curves.

 [1] A. Bertram, Moduli of rank-$2$ vector bundles, theta divisors, and the geometry of curves in projective space, J. Differential Geom., 35, (1992), 429–469. [2] Singularities and syzygies of secant varieties of nonsingular projective curves. Invent. Math. (2020) 222: 615-665. [3] Some results on secant varieties leading to a geometric flip construction. Compositio Math. (2001) 125: 263-282.
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