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doi: 10.3934/era.2021055
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## On blowup of secant varieties of curves

 1 Department of Mathematics, University Illinois at Chicago, 851 South Morgan St., Chicago, IL 60607, USA 2 Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, USA 3 Department of Mathematics, Sogang University, 35 Beakbeom-ro, Mapo-gu, Seoul 04107, Republic of Korea

Received  March 2021 Early access July 2021

Fund Project: J. Park was partially supported by the National Research Foundation (NRF) funded by the Korea government (MSIT) (NRF-2021R1C1C1005479)

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. Electronic Research Archive, doi: 10.3934/era.2021055
##### References:
 [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.  Google Scholar [2] L. Ein, W. Niu and J. Park, Singularities and syzygies of secant varieties of nonsingular projective curves, Invent. Math., 222 (2020), 615-665.  doi: 10.1007/s00222-020-00976-5.  Google Scholar [3] P. Vermeire, Some results on secant varieties leading to a geometric flip construction, Compositio Math., 125 (2001), 263-282.  doi: 10.1023/A:1002663915504.  Google Scholar

show all references

##### References:
 [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.  Google Scholar [2] L. Ein, W. Niu and J. Park, Singularities and syzygies of secant varieties of nonsingular projective curves, Invent. Math., 222 (2020), 615-665.  doi: 10.1007/s00222-020-00976-5.  Google Scholar [3] P. Vermeire, Some results on secant varieties leading to a geometric flip construction, Compositio Math., 125 (2001), 263-282.  doi: 10.1023/A:1002663915504.  Google Scholar
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