论文信息 - Elementary Theory of Del Pezzo Surfaces

Elementary Theory of Del Pezzo Surfaces

Del Pezzo surfaces are certain algebraic surfaces in projective n-space of degree n. They contain an interesting configuration of lines and have a rational parametrization. We give an overview of the classification with an emphasis on algorithmic constructions (e.g. of the parametrization), on explicit computations, and on real algebraic geometry.

Josef Schicho

[1] Rimvydas Krasauskas,et al. Toric Surface Patches , 2002, Adv. Comput. Math..

[2] On the structure of polarized manifolds with total deficiency one, II , 1980 .

[3] Real forms of smooth del Pezzo surfaces. , 1987 .

[4] Joe W. Harris,et al. Algebraic Geometry: A First Course , 1995 .

[5] Arthur Cayley. VII. A memoir on cubic surfaces , 1869, Philosophical Transactions of the Royal Society of London.

[6] Josef Schicho,et al. Rational Parametrization of Surfaces , 1998, J. Symb. Comput..

[7] G. Jung,et al. Ricerche sui sistemi lineari di curve algebriche di genere qualunque , 1887 .

[8] C. Ciliberto,et al. The antibirational involutions of the plane and the classification of real del Pezzo surfaces , 2002 .

[9] Annibale Comessatti,et al. Fondamenti per la geometria sopra le suerficie razionali dal punto di vista reale , 1912 .

[10] F. Conforto. Le superficie razionali , 1939 .

[11] Josef Schicho,et al. Rational parametrization of real algebraic surfaces , 1998, ISSAC '98.

[12] Robert Silhol,et al. Real Algebraic Surfaces , 1989 .

[13] Joe W. Harris,et al. Principles of Algebraic Geometry , 1978 .

[14] C. Wall,et al. On the Classification of Cubic Surfaces , 1979 .