Nonrational nodal quartic threefolds
نویسندگان
چکیده
منابع مشابه
Nonrational Nodal Quartic Threefolds
The Q-factoriality of a nodal quartic 3-fold implies its non-rationality. We prove that a nodal quartic 3-fold with at most 8 nodes is Q-factorial, and we show that a nodal quartic 3-fold with 9 nodes is not Q-factorial if and only if it contains a plane. However, there are non-rational non-Q-factorial nodal quartic 3-folds in P. In particular, we prove the non-rationality of a general non-Q-fa...
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It is well-known that a nonsingular minimal cubic surface is birationally rigid; the group of its birational selfmaps is generated by biregular selfmaps and birational involutions such that all relations between the latter are implied by standard relations between reflections on an elliptic curve. It is also known that a factorial nodal quartic threefold is birationally rigid and its group of b...
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∼= P, where g(x, y, z) = 0 is a homogeneous equation of the curve Z and (λ, μ) ∈ P. Then a general curve in P is birational to an elliptic curve. Remark 1.1. The construction of pencil P can be generalized to the case when C has at most ordinary double points and the points P1, · · · , P9 are not necessarily distinct (see [3]). The pencil P is called a standard Halphen pencil. Definition 1.2. A...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2006
ISSN: 0030-8730
DOI: 10.2140/pjm.2006.226.65