Projectively normal adjunction surfaces

Authors:
Marco Andreatta and Edoardo Ballico

Journal:
Proc. Amer. Math. Soc. **112** (1991), 919-924

MSC:
Primary 14J25

MathSciNet review:
1057947

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Abstract: On a projective surface polarized by a very ample line bundle one can consider the adjoint bundles and the adjunction mappings associated to them. Suppose these mappings are embeddings (it is well known when this is the case: see [So-VdV]). We prove that these embeddings are projectively normal for and we describe some counterexamples for . For we show that the ideals of the image of are generated by quadrics.

**[Ba-El1]**E. Ballico and Ph. Ellia,*On degeneration of projective curves*, Algebraic geometry—open problems (Ravello, 1982) Lecture Notes in Math., vol. 997, Springer, Berlin, 1983, pp. 1–15. MR**714739**, 10.1007/BFb0061634**[Ba-E12]**E. Ballico and Ph. Ellia,*On the existence of curves with maximal rank in 𝑃ⁿ*, J. Reine Angew. Math.**397**(1989), 1–22. MR**993216****[Gr]**Mark L. Green,*Koszul cohomology and the geometry of projective varieties*, J. Differential Geom.**19**(1984), no. 1, 125–171. MR**739785****[Mu]**Oscar Zariski,*The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface*, Ann. of Math. (2)**76**(1962), 560–615. MR**0141668****[Sel]**Fernando Serrano,*The adjunction mappings and hyperelliptic divisors on a surface*, J. Reine Angew. Math.**381**(1987), 90–109. MR**918842**, 10.1515/crll.1987.381.90**[Se2]**-,*Divisors of bielliptic surfaces and embeddings in*preprint.**[So-VdV]**Andrew John Sommese and A. Van de Ven,*On the adjunction mapping*, Math. Ann.**278**(1987), no. 1-4, 593–603. MR**909240**, 10.1007/BF01458083

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1057947-X

Keywords:
Adjoint bundle,
adjunction mapping,
projective normality

Article copyright:
© Copyright 1991
American Mathematical Society