Gudkovの論文 | K3 surfaces with involutions

K3 surfaces with involutions

Local and global Torelli theorems for complex K3 surfaces, periods of K3 surfaces, non-symplectic holomorphic involutions, anti-holomorphic involutions, Hilbert schemes of K3 surfaces, Nikulin's lattice theory, lattice-polarized K3 surfaces. . .


D.A. Gudkov,
Construction of a curve of the 6th order of type $\dfrac{1}{5}5$,
Izv. Vyssh. Uchebn. Zaved. Mat., {\bf 3 (130)} (1973), 28--36.


D.A. Gudkov, A.D. Krakhnov,
Periodicity of the Euler characteristic of real algebraic (M-1)-varieties,
Funkt. Anal. Prilozhen., {\bf 7--2} (1973), 15--19.

= Funct. Anal. Appl., {\bf 7} (1973), 98--102.


D.A. Gudkov,
The topology of real projective algebraic varieties,
Usp. Mat. Nauk, 29-4 (1974), 3--79

= Russ. Math. Surveys, {\bf 29--4} (1974), 1--79.


D.A. Gudkov, G.A. Utkin,
The topology of curves of the sixth order and surfaces of the fourth order,

Gor'kov. Gos. Univ. Uchen. Zap., {\bf 87} (1969), 3--213.

= Nine papers on Hilbert's 16th problem,
Amer. Math. Soc. Transl. (2) {\bf 112} (1978).



D.A. Gudkov,
On the topology of algebraic curves on a hyperboloid,
Usp. Mat. Nauk, {\bf 34--6} (1979), 26--32.

= Russ. Math. Surveys, {\bf 34--6} (1979), 27--35.

ここで,hyperboloidとは,RP^3の中のnonsingular quadric (2次曲面)で,トーラスに同相なもののこと.これは,RP^1 x RP^1 とみなせる.球面S^2に同相な場合は,ellipsoidと呼ばれる.ほかには,空集合の場合がある(同じ定義方程式の複素零点集合は空でないにも関わらず)

Gudkovのこの論文では,RP^2上の代数曲線を,RP^2からhyperboloidへの2次変換(双有理変換の一種)によってhyperboloid上に写すことにより,hyperboloid上の曲線を構成している.その際には,order がどのように変化するかについての公式が重要である.



D.A. Gudkov,
Generalization of a theorem of Brusotti for curves on a surface of second order,

Funct. Anal. Appl., {\bf 14} (1980), 15--18.