Projective normality of abelian surfaces of type (1, 2d)
نویسنده
چکیده
We show that an abelian surface embedded in P by a very ample line bundle L of type (1, 2d) is projectively normal if and only if d ≥ 4. This completes the study of the projective normality of abelian surfaces embedded by complete linear systems. Mathematics Subject Classifications (2000): Primary, 14K05; secondary, 14N05, 14E20.
منابع مشابه
. A G ] 1 4 Ju n 20 04 Some results about the projective normality of abelian varieties . Luis Fuentes Garćıa
We reduce the problem of the projective normality of polarized abelian varieties to check the rank of very explicit matrices. This allow us to prove some results on normal generation of primitive line bundles on abelian threefolds and fourfolds. We also give two situations where the projective normality always fails. Finally we make some conjecture. Mathematics Subject Classifications (2000): P...
متن کامل$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings
A module is said to be $PI$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of $PI$-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...
متن کاملProjective Normality of Abelian Varieties
We show that ample line bundles L on a g-dimensional simple abelian variety A, satisfying h0(A,L) > 2g · g!, give projective normal embeddings, for all g ≥ 1.
متن کاملOn Abelian Families and Holomorphic Normal Projective Connections
1.) Pm(C), 2.) smooth abelian families, 3.) manifolds with universal covering Bm(C). Here Bm(C) denotes the ball in C , the non compact dual of Pm(C) in the sense of hermitian symmetric spaces. The second point inlcudes the flat case of an abelian manifold. Any compact Riemann surface admits a holomorphic normal projective connection, this is the famous uniformization theorem. Kobayashi and Och...
متن کاملOn the Projective Normality of Smooth Surfaces of Degree Nine
The projective normality of smooth, linearly normal surfaces of degree 9 in P is studied. All non projectively normal surfaces which are not scrolls over a curve are classified. Results on the projective normality of surface scrolls are also given.
متن کامل