Mapping threefolds onto three-quadrics
نویسنده
چکیده
We prove that the degree of a nonconstant morphism from a smooth projective 3-fold X with Néron-Severi group Z to a smooth 3-dimensional quadric is bounded in terms of numerical invariants of X. In the special case where X is a 3-dimensional cubic we show that there are no such morphisms. The main tool in the proof is Miyaoka’s bound on the number of double points of a surface.
منابع مشابه
On Calabi-yau Threefolds with Large Nonabelian Fundamental Groups
In this short note we construct Calabi-Yau threefolds with nonabelian fundamental groups of order 64 as quotients of the small resolutions of certain complete intersections of quadrics in P that were first considered by M. Gross and S. Popescu.
متن کاملClassification of Free Actions on Complete Intersections of Four Quadrics
In this paper we classify all free actions of finite groups on Calabi-Yau complete intersection of 4 quadrics in P, up to projective equivalence. We get some examples of smooth CalabiYau threefolds with large nonabelian fundamental groups. We also observe the relation between some of these examples and moduli of polarized abelian surfaces.
متن کاملHyperelliptic and Trigonal Fano Threefolds
We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein singularities which are not the intersection of quadrics.
متن کاملHopf Mappings for Complex Quaternions
The natural mapping of the right quaternion vector space H onto the quaternion projective line (identified with the four-sphere) can be defined for complex quaternions H ⊗R C as well. We discuss its exceptional set, the fiber subspaces, and how the linear automorphism groups of two-dimensional quaternion vector spaces and modules induce groups of projective automorphisms of the image quadrics.
متن کاملOn Rationality of Nonsingular Threefolds with a Pencil of Del Pezzo Surfaces of Degree 4
We prove a criterion of nonsingularity of a complete intersection of two fiberwise quadrics in P P 1 (O(d 1) ⊕. .. ⊕ O(d 5)). As a corollary we derive the following addition to the Alexeev theorem on rationality of standard Del Pezzo fibrations of degree 4 over P 1 : we prove that any fibration of this kind with the topological Euler characteristic χ(X) = −4 is rational.
متن کامل