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A complex surface $S$ is said to be isogenous to a product if $S$ is a quotient $S=(C_1 times C_2)/G$ where the $C_i$s are curves of genus at least two, and $G$ is a finite group acting freely on $C_1 times C_2$. In this paper we classify all regular surfaces isogenous to a product with $chi(mathcal O_S) = 2$ under the assumption that the action of $G$ is unmixed i.e. no element of $G$ exchange the factors of the product $C_1 times C_2$.
Let $S$ be a surface isogenous to a product of curves of unmixed type. After presenting several results useful to study the cohomology of $S$ we prove a structure theorem for the cohomology of regular surfaces isogenous to a product of unmixed type w
Let $(S,mathcal L)$ be a smooth, irreducible, projective, complex surface, polarized by a very ample line bundle $mathcal L$ of degree $d > 25$. In this paper we prove that $chi (mathcal O_S)geq -frac{1}{8}d(d-6)$. The bound is sharp, and $chi (mathc
We give new contributions to the existence problem of canonical surfaces of high degree. We construct several families (indeed, connected components of the moduli space) of surfaces $S$ of general type with $p_g=5,6$ whose canonical map has image $Si
In this paper we study emph{threefolds isogenous to a product of mixed type} i.e. quotients of a product of three compact Riemann surfaces $C_i$ of genus at least two by the action of a finite group $G$, which is free, but not diagonal. In particular
In this paper, we classify the minimal surfaces of general type with $chi=5$, $K^{2}=9$ whose canonical map is composed with an involution. We obtain 6 families, whose dimensions in the moduli space are 28, 27, 33, 32, 31 and 32 respectively. Among t