## Effective degree bounds for generalized Gauss map images.(English)Zbl 1388.14140

Oguiso, Keiji (ed.) et al., Higher dimensional algebraic geometry. In honour of Professor Yujiro Kawamata’s sixtieth birthday. Proceedings of the conference, Tokyo, Japan, January 7–11, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-046-4/hbk). Advanced Studies in Pure Mathematics 74, 203-235 (2017).
Summary: 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.
For the entire collection see [Zbl 1388.14012].

### MSC:

 14N05 Projective techniques in algebraic geometry 14M15 Grassmannians, Schubert varieties, flag manifolds 14N15 Classical problems, Schubert calculus 14J40 $$n$$-folds ($$n>4$$)