Birational Models of Mori Fibre Spaces, Pliability and Cox Rings
نویسندگان
چکیده
We study birational transformations of certain fibtations of degree 4 del Pezzo surfaces over P, into other Mori fibre spaces, using Cox rings. We show that these Mori fibre spaces have a (relatively) big pliability although they are not rational. Our methods can be applied to study birational geometry of Mori dream spaces with low rank Cox ring.
منابع مشابه
Birational Geometry of 3-fold Mori Fibre Spaces
In this paper we study standard 3-fold conic bundles X/P and stable cubic del Pezzo fibrations X/P. These are the key examples of 3-fold Mori fibre spaces (Mfs). We begin systematically to chart the geography of these varieties, namely the classification of their deformation families and discrete invariants. Given a 3-fold Mfs X/S, we aim to understand the set of all Mfs Y/T with X birational t...
متن کاملBirational geometry of hypersurfaces in products of projective spaces
We study the birational properties of hypersurfaces in products of projective spaces. In the case of hypersurfaces in P × P, we describe their nef, movable and effective cones and determine when they are Mori dream spaces. Using this, we give new simple examples of non-Mori dream spaces and analogues of Mumford’s example of a strictly nef line bundle which is not ample.
متن کاملRecent Results in Higher-Dimensional Birational Geometry
This note surveys some recent results on higher-dimensional birational geometry, summarising the views expressed at the conference held at MSRI in November 1992. The topics reviewed include semistable flips, birational theory of Mori fiber spaces, the logarithmic abundance theorem, and effective base point freeness.
متن کاملBirational Geometry of the Space of Rational Curves in Homogeneous Varieties
In this thesis, we investigate the birational geometry of the space of rational curves in various homogeneous spaces, with a focus on the quasi-map compactification induced by the Quot and Hyperquot functors. We first study the birational geometry of the Quot scheme of sheaves on P1 via techniques from the Mori program, explicitly describing its associated cones of ample and effective divisors ...
متن کاملRims-1706 Birational Unboundedness of Log Terminal Q-fano Varieties and Rationally Connected Strict Mori Fiber Spaces
In this paper, we show that (Q-factorial and log terminal) Q-Fano varieties with Picard number one are birationally unbounded in each dimension ≥ 3. This result has been settled for 3-folds by J. Lin and n-folds with n ≥ 6 by the author. We also prove that rationally connected Mori fiber spaces are birationally unbounded even if we fix dimensions of both total and base spaces.
متن کامل