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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. EinW. 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. EinW. 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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