## Pacific Journal of Mathematics

### Classification of algebraic surfaces with sectional genus less than or equal to six. I. Rational surfaces.

Elvira Laura Livorni

#### Article information

Source
Pacific J. Math., Volume 113, Number 1 (1984), 93-114.

Dates
First available in Project Euclid: 8 December 2004

https://projecteuclid.org/euclid.pjm/1102709380

Mathematical Reviews number (MathSciNet)
MR745598

Zentralblatt MATH identifier
0573.14013

Subjects
Primary: 14J26: Rational and ruled surfaces
Secondary: 14J10: Families, moduli, classification: algebraic theory

#### Citation

Livorni, Elvira Laura. Classification of algebraic surfaces with sectional genus less than or equal to six. I. Rational surfaces. Pacific J. Math. 113 (1984), no. 1, 93--114. https://projecteuclid.org/euclid.pjm/1102709380

#### References

• [A+F] A. Andreotti and T. Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math., 69 (1959), 713-717.
• [Ba] H. F. Baker,Principles of Geometry, V, CambridgeUniversityPress,1933.
• [Bo] R. Bott, On a theorem of Lefschetz, Michigan Math. J., 6, 211-216.
• [Fu] T. Fujita, On the structure of polarized varieties with -genera zero, J. Fac. Sci. Univ. Tokyo,22 (1975),103-115.
• [G-f H] P. A. Griffiths and J. Harris, Residues and zero cycles on algebraic varieties, Ann. of Math., 108(1978), 461-555.
• [Ha] R. Hartshorne, Algebraic Geometry, Springer-Verlag,New York, 1977.
• [Io] P. Ionescu, An enumerationof all smoothprojective varieties of degree5 and 6, Preprint, Series in Mathematics Nr. 74/1981.
• [N] M. Nagata, On rational surfaces I, Mem. Coll. Sci. Kyoto, (A) 32 (1960), 351-370.
• [R] L. Roth, On theprojective classificationof surfaces, Proc. London Math. Soc, (2)42(1937), 142-170.
• [Sa] B. Saint-Donat, On PetriJs analysis of the linear system of quadrics through a canonicalcurve, Math. Ann.,206 (1973),157-175.
• [Sk] F. Sakai, Semi-stablecurves on algebraic surfaces and logarithmic pluricanoni- cal maps, Sonderforschungsbereich Theoritische Mathematik 40, Universitat Bonn.
• [S4-R] J. G. Semple and L. Roth, Introduction to Algebraic Geometry, Clarendon Press, Oxford, 1949.
• [So] A. J. Sommese,Hyperplane sections of projective surfaces I--The adjunction mapping, Duke Math. J.,46 No. 2(1979).
• [So] A. J. Sommese, On the minimality of hyperplane sections of projective threefolds, J. Reine Angew. Math., 329 (1981), 16-41.

• Elvira Laura Livorni. Classification of algebraic surfaces with sectional genus less than or equal to six. {II}. Ruled surfaces with {${\r dim}\,\phi\sb {K\sb Xøtimes L}(X)=1$}. II [MR 88d:14023] Canad. J. Math. 38 1986 5 1110--1121.
• Elvira Laura Livorni. Classification of algebraic surfaces with sectional genus less than or equal to six. {III}. Ruled surfaces with {${\r dim}\phi\sb {K\sb Xøtimes L}(X)=2$}. III [MR 88d:14024] Math. Scand. 59 1986 1 9--29.