Related papers: Algebraic Surfaces Holomorphically Dominable by C2

Using the theory of cohomology support locus, we give a necessary condition for the Albanese map of a smooth projective surface being a submersion. More precisely, assuming the cohomology support locus of any finite abelian cover of a…

In this paper we classify the topological invariants of the possible branch loci of a smooth double cover $f:X\rightarrow Y$ of a K3 surface $Y$. We describe some geometric properties of $X$ which depend on the properties of the branch…

In this paper we prove that a normal Gorenstein surface dominated by the projective plane P^2 is isomorphic to a quotient P^2/G, where G is a finite group of automorphisms of P^2 (except possibly for one surface V_8'). We can completely…

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We classify singular Q-homology planes which are C^1- or C*-ruled. We analyze their completions, the number of different rulings, the number of…

Let $Y$ be an algebraic manifold of dimension 3 with $H^i(Y, \Omega^j_Y)=0$ for all $j\geq 0$, $i>0$ and $h^0(Y, {\mathcal{O}}_Y) > 1$. Let $X$ be a smooth completion of $Y$ such that the boundary $X-Y$ is the support of an effective…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

Let F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the DG-Lie algebra RHom(F,F) of derived endomorphisms of F is formal. The proof is based on the study of equivariant $L_{\infty}$ minimal models…

Let $X$ be a smooth complex projective algebraic variety of maximal Albanese dimension. We give a characterization of $\kappa (X)$ in terms of the set $V^0(X,\omega_{X})$ $:=\{P\in {\text{\rm Pic}}^0(X)|h^0(X, \omega_X \otimes P) \ne 0\}$.…

The hypergeometric functions ${}_nF_{n-1}$ are higher transcendental functions, but for certain parameter values they become algebraic, because the monodromy of the defining hypergeometric differential equation becomes finite. It is shown…

The famous Nakayama conjecture states that the dominant dimension of a non-selfinjective finite dimensional algebra is finite. In \cite{Yam}, Yamagata stated the stronger conjecture that the dominant dimension of a non-selfinjective finite…

A wealth of geometric and combinatorial properties of a given linear endomorphism $X$ of $\R^N$ is captured in the study of its associated zonotope $Z(X)$, and, by duality, its associated hyperplane arrangement ${\cal H}(X)$. This…

For a geometrically rational surface X over an arbitrary field of characteristic different from 2 and 3 that contains all roots of 1, we show that either X is birational to a product of a projective line and a conic, or the group of…

This paper investigates the geometry of smooth canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the…

Let $X$ be a compact K\"ahler manifold and let $f:X\rightarrow X$ be a dominant rational map which is 1-stable. Let $\lambda_1$ and $\lambda_2$ be the first and second dynamical degrees of $f$. If $\lambda_1^2>\lambda_2$, then we show that…

Let $S$ be a smooth projective surface over $\mathbb{C}$ and $S^{[n]}$ be the Hilbert scheme of $n$ points over $S$, for any positive integer $n$. Let ${\bf a}=(n_1,\ldots,n_r)$ and ${\bf b}=(m_1,\ldots,m_s)$ be two distinct partitions of…

Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic structure gives a basic kind of $A$-graded algebras…

We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the…

The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional algebra may be absolutely rigid in the classical…

We study the classification of the pairs $(N, \,X)$ where $N$ is a Stein surface and $X$ is a complete holomorphic vector field with isolated singularities on $N$. We describe the role of transverse sections in the classification of $X$ and…

We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a…