Related papers: Mixed Threefolds Isogenous to a Product

A threefold isogenous to a product of curves $X$ is a quotient of a product of three compact Riemann surfaces of genus at least two by the free action of a finite group. In this paper we study these threefolds under the assumption that the…

We study canonical and pluricanonical maps of varieties isogenous to a product of curves, i.e., quotients of the form $X = (C_1 \times \dots \times C_n)/G$ with $g(C_i)\ge 2$ and $G$ acting freely. For this purpose, we provide a technical…

In this note, we study rigid complex manifolds that are realized as quotients of a product of curves by a free action of a finite group. They serve as higher-dimensional analogues of Beauville surfaces. Using uniformization, we outline the…

A smooth algebraic surface $S$ is said to be \emph{isogenous to a product of unmixed type} if there exist two smooth curves $C, F$ and a finite group $G$, acting faithfully on both $C$ and $F$ and freely on their product, so that $S=(C…

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…

Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.

We classify all the surfaces with p_g = q = 0 which admit an unramified covering which is isomorphic to a product of curves. Beyond the trivial case \PP^1 x \PP^1 we find 17 families which we explicitly describe. We reduce the problem to a…

We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian mani\-folds are either conformally flat, or triple products, \emph{i.e.} locally…

Let $\mathcal{X}$ be a smooth Fano threefold over the complex numbers of Picard rank $1$ with finite automorphism group. We give numerical restrictions on the order of the automorphism group $\mathrm{Aut}(\mathcal{X})$ provided the genus…

We give a method for the computation of the plurigenera of a product-quotient manifold. We give two different types of applications to it: to the construction of Calabi-Yau threefolds and to the determination of the minimal model of a…

The triple-cup product form $\mu$ is a classical invariant of $3$-manifolds, determining the cohomology ring up to torsion. Given a closed, connected, oriented $3$-manifold $M$, we describe an explicit formula for computing $\mu$ from a…

In this note, we give explicit examples of compact complex 3-folds which admit automorphisms that are isotopic to the identity through C $\infty$-diffeomorphisms but not through biholomorphisms. These automorphisms play an important role in…

We give necessary and sufficient conditions for a closed smooth 6-manifold N to be diffeomorphic to a product of a surface F and a simply connected 4-manifold M in terms of basic invariants like the fundamental group and cohomological data.…

Let $G$ be a finite group acting on a connected compact surface $\Sigma$, and $M$ be an integer homology 3-sphere. We show that if each element of $G$ is extendable over $M$ with respect to a fixed embedding $\Sigma\rightarrow M$, then $G$…

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…

We show that the bigraded quasi-isomorphism type of the bigraded, bidifferential algebra of forms on a compact K\"ahler manifold generally contains more information than the de Rham cohomology algebra with its real Hodge structure. More…

Let $C$ be a smooth projective curve and $G$ a finite subgroup of $\mathrm{Aut}(C)^2\rtimes \mathbb Z_2$ whose action is \textit{mixed}, i.e.~there are elements in $G$ exchanging the two isotrivial fibrations of $C\times C$. Let…

We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and…

Using elementary techniques from Geometric Analysis, Partial Differential Equations, and Abelian $C^*$ Algebras, we uncover a novel, yet familiar, global geometric invariant -- namely the indexed set of integrals of triple products of…

In this article we consider compact Riemann surfaces that are uniquely determined by the property of possessing a group of automorphisms of a prescribed order, strengthening uniqueness results proved by Nakagawa. More precisely, we deal…