References
[BM] Bayer, D., Mumford, D.: What can be computed in algebraic geometry? Proceedings of Computer Algebra as a Tool for Research in Mathematics and Physics, Courant Institute, April 1984
[Ca] Castelnuovo, G.: Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica. Rend. Circ. Mat. Palermo7, 89–110 (1893)
[En] Enriques, F.: Le superficie algebriche. Bologna: Zanichelli 1949
[Fr] Franchetta, A.: Sulla curva doppia della proiezione di una superficie generale delloS 4 da un punto generico su unoS 3. Rend. R. Acc. d'Italia (1941); Rend. dell'Acc. dei Lincei2 (8), 276–280 (1947)
[FL] Fulton, W., Lazarsfeld, R.: connectivity and its applications in algebraic geometry. In: Algebraic Geometry (Proceeding of the Midwest Algebraic Geometry conference, Chicago Circle 1980). Springer Lect. Notes862, 26–92 (1981)
[GH] Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley Interscience 1978
[GLP] Gruson, L., Lazarsfeld, R., Peskine, C.: On a theorem of Castelnuovo, and the equations defining space curves. Invent. Math.72, 491–506 (1983).
[H] Hartshorne, R.: Algebraic geometry. New York-Heidelberg-Berlin: Springer 1977
[Kl] Kleiman, S.: The enumerative theory of singularities. In: Real and complex singularities, Oslo 1976 (P. Holm, ed.), pp. 297–396 Groningen: Sijthoff & Noordhoff 1978
[LV] Lazarsfeld, R., Van de Ven, A.: Recent work of F.L. Zak. Proceedings of DMV Seminar, Düsseldorf 1982
[Mo] Moishezon, B.: Complex surfaces and connected sums of complex projective planes. Springer Lect. Notes Math.603, 1–234 (1977)
[Mu] Mumford, D.: Varieties defined by quadratic equations In: Questions on algebraic varieties, Corso C.I.M.E. 1969, pp. 30–100, Rome: Cremonese 1970
[Pe] Persson, U.: Double coverings and surfaces of general type. In: Algebraic Geometry, Proceedings, Tromsø 1977 (L. Olson, ed.) Springer Lect. Notes Math.687, 168–195 (1978)
[P] Piene, R.: Some formulas for a surface in ℙ3. (In same) pp. 196–235
[PR] Piene, R., Ronga, F.: A geometric approach to the arithmetic genus of a projective manifold of dimension three. Topology20, 179–190 (1981)
[Pi] Pinkham, H.: Factorization of birational maps in dimension 3 (Part 2). Proc. Symp. Pure Math.40, 343–371 (1983)
[R] Rao, P.: Liaison equivalence classes. Math. Ann.258, 169–173 (1981).
[Ro] Roberts, J.: Hypersurfaces with nonsingular normalization and their double loci. J. Algebra53, 253–267 (1978)
[SR] Semple, J.G., Roth, L.: Introduction to algebraic geometry. Oxford: Clarendon Press 1949
[Se] Severi, F.: Intorno ai punti doppi impropri di una superficie generale dello spazio a quattro dimensioni e a'suoi punti tripli apparenti. Rend. Circ. Mat. Palermo15, 33–51 (1901)
[Wi] Wilson, P.M.H.: On blowing up conductor ideals. Math. Proc. Camb. Philos. Soc.83, 445–450 (1978)
[Z] Zak, F.L.: Projections of algebraic varieties. Math. USSR, Sb.44, 535–544 (1983)
[Za1] Zariski, O.: Algebraic surfaces (Second supplemented edition) New York-Heidelberg-Berlin: Springer 1971
[Za2] Zariski, O.: An introduction to the theory of algebraic surfaces. Springer Lect. Notes Math.83, 1–100 (1972)
Author information
Authors and Affiliations
Additional information
To my father, Francis H. Pinkham
Partially supported by N.S.F. grant MC5-8005802 at Columbia University, USA
Rights and permissions
About this article
Cite this article
Pinkham, H.C. A Castelnuovo bound for smooth surfaces. Invent Math 83, 321–332 (1986). https://doi.org/10.1007/BF01388966
Issue Date:
DOI: https://doi.org/10.1007/BF01388966