On blowup of secant varieties of curves

Lawrence Ein; Wenbo Niu; Jinhyung Park; Lawrence Ein; Wenbo Niu; Jinhyung Park

doi:10.3934/era.2021055

Electronic Research Archive

2021, Volume 29, Issue 6: 3649-3654. 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: 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.
- Secant variety,
- secant sheaf,
- secant bundle
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

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Abstract

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.

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.
[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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