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On multisecants and the Green-Lazarsfeld index of projective varieties

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Abstract

It is well known that a nondegenerate projective subvariety \({X \subset \mathbb {P}^r}\) of degree d and codimension c > 1 has minimal degree (i.e., d = c + 1) if and only if index(X) ≥ c if and only if X has no multisecant c-space. In this paper we extend this result by classifying varieties with index(X) ≥ c − s or with no multisecant (c − s)-space for s = 1 and 2.

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Authors and Affiliations

  1. School of Mathematics, KIAS (Korea Institute for Advanced Study), 207-43, Cheongnyangni-dong, Dongdaemun-Gu, Seoul, 103-722, Republic of Korea

    Wanseok Lee & Youngho Woo

  2. Department of Mathematics, Korea University, Seoul, 136-701, Republic of Korea

    Euisung Park

Authors
  1. Wanseok Lee
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  2. Euisung Park
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  3. Youngho Woo
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Correspondence to Euisung Park.

Additional information

The first and third named authors were supported by the National Researcher program 2010-0020413 of NRF and MEST. The second named author was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (No. 20090073305).

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Lee, W., Park, E. & Woo, Y. On multisecants and the Green-Lazarsfeld index of projective varieties. Arch. Math. 96, 525–530 (2011). https://doi.org/10.1007/s00013-011-0270-1

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  • DOI: https://doi.org/10.1007/s00013-011-0270-1

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