Degeneration of Kunev surfaces. I
A Kunev surface is a minimal surface X of general type with \(p_ g=c^ 2_ 1=1\) having an involution \(\alpha\) : \(X\to X\) such that \(Y'=X/\alpha\) is a K3 surface with rational double points and the bicanonical map of X is a Galois cover of \({\mathbb{P}}^ 2\) factoring through \(Y'\). In the note under review the author formulates two theorems describing degenerations of Kunev surfaces over a fixed K3 surface. Using these theorems, the author gives a uniform explanation for the failure of the Torelli theorem for the period map \(\Phi_ 2\) of the pure second cohomology of Kunev surfaces and elliptic surfaces with \(p_ g=1\) and \(q=0, 1\). There are no proofs.
scientific article; zbMATH DE number 4144146