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For a binary quartic form $phi$ without multiple factors, we classify the quartic K3 surfaces $phi(x,y)=phi(z,t)$ whose Neron-Severi group is (rationally) generated by lines. For generic binary forms $phi$, $psi$ of prime degree without multiple factors, we prove that the Neron-Severi group of the surface $phi(x,y)=psi(z,t)$ is rationally generated by lines.
In this paper we extend the well known theorem of Angelo Lopez concerning the Picard group of the general space projective surface containing a given smooth projective curve, to the intermediate Neron-Severi group of a general hypersurface in any smooth projective variety.
Let $Z$ be a closed subscheme of a smooth complex projective complete intersection variety $Ysubseteq Ps^N$, with $dim Y=2r+1geq 3$. We describe the Neron-Severi group $NS_r(X)$ of a general smooth hypersurface $Xsubset Y$ of sufficiently large degree containing $Z$.
Let $X$ be a minimal surface of general type and maximal Albanese dimension with irregularity $qgeq 2$. We show that $K_X^2geq 4chi(mathcal O_X)+4(q-2)$ if $K_X^2<frac92chi(mathcal O_X)$, and also obtain the characterization of the equality. As a con
Let ${P_i}_{1 leq i leq r}$ and ${Q_i}_{1 leq i leq r}$ be two collections of Brauer Severi surfaces (resp. conics) over a field $k$. We show that the subgroup generated by the $P_is$ in $Br(k)$ is the same as the subgroup generated by the $Q_is$ iff
We prove that a reduced and irreducible algebraic surface in $mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalization map of a surface, we give constructive existence results for even degrees.