Advanced Studies in Pure Mathematics

Effective degree bounds for generalized Gauss map images

Gordon Heier and Shigeharu Takayama

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Abstract

We establish effective uniform degree bounds for the generalized Gauss map images of an embedded projective variety $X \subset \mathbb P^N$ in terms of numerical invariants such as $\dim X,$ $\deg X$ and $N$. This can be seen as a generalization of a classical Castelnuovo type bound.

Article information

Source
Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, K. Oguiso, C. Birkar, S. Ishii and S. Takayama, eds. (Tokyo: Mathematical Society of Japan, 2017), 203-235

Dates
Received: 30 June 2013
Revised: 31 March 2014
First available in Project Euclid: 23 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540319489

Digital Object Identifier
doi:10.2969/aspm/07410203

Mathematical Reviews number (MathSciNet)
MR3791215

Zentralblatt MATH identifier
1388.14140

Subjects
Primary: 14N05: Projective techniques [See also 51N35] 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14N15: Classical problems, Schubert calculus 14J40: $n$-folds ($n > 4$)

Citation

Heier, Gordon; Takayama, Shigeharu. Effective degree bounds for generalized Gauss map images. Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, 203--235, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07410203. https://projecteuclid.org/euclid.aspm/1540319489


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