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

Heier, Gordon; Takayama, Shigeharu

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 (\(n>4\))