相关论文: Logarithmic multicanonical systems of smooth affin…

We consider the multicanonical systems $\vert mK_{S}\vert$ of quasi-elliptic surfaces with Kodaira dimension $1$ in characteristic 2. We show that for any $m \geq 6$ $\vert mK_{S}\vert$ gives the structure of quasi-elliptic fiber space, and…

This paper considers the family $\mathscr{S}_0$ of smooth affine factorial surfaces of logarithmic Kodaira dimension 0 with trivial units over an algebraically closed field $k$. Our main result (Theorem 4.1) is that the number of…

Let $(S,D)$ be a minimal log pair of general type with $S$ a smooth projective surface and $D$ a simple normal corssing reduced divisor on $S$. We assume that its log canonial linear system $|K_S+D|$ is composed of a penciel, let $f\colon…

We consider the multicanonical systems $|mK_S|$ of quasi-elliptic surfaces with Kodaira dimension $1$ in characteristic 3. We show that for any $m \geq 5$ $|mK_S|$ gives the structure of quasi-elliptic fiber space, and the number $5$ is…

We prove that for any smooth complex projective threefold of Kodaira dimension one, the $m$-th pluricanonical map is birational to the Iitaka fibration for every $m\geq5868$ and divisible by $12$.

The main result is that a quasi-projective surface has negative log Kodaira dimension (i.e. no log pluricanonical sections) iff it is dominated by images of the affine line. This follows from our main intermediate result, that the smooth…

In this paper, we study the adjoint foliated structures of the form $K_{\mathcal{F}}+D$ on algebraic surfaces, with particular focus on their minimal and canonical models. We investigate the effective behavior of the multiple linear system…

This paper is devoted to the study of affine quaternionic manifolds and to a possible classification of all compact affine quaternionic curves and surfaces. It is established that on an affine quaternionic manifold there is one and only one…

We study pluricanonical systems on smooth projective varieties of positive Kodaira dimension, following the approach of Hacon-McKernan, Takayama and Tsuji succesfully used in the case of varieties of general type. We prove a uniformity…

We give a corrected statement of the theorem of Gurjar and Miyanishi, which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such surfaces by…

We study the set ${\mathcal P}_S$ consisting of all branched holomorphic projective structures on a compact Riemann surface $X$ of genus $g \geq 1$ and with a fixed branching divisor $S:= \sum_{i=1}^d n_i\cdot x_i$, where $x_i \in X$. Under…

For a normal subvariety $V$ of ${\bf C}^n$ with a good ${\bf C}^*$-action we give a simple characterization for when it has only log canonical, log terminal or rational singularities. Moreover we are able to give formulas for the…

We construct a linearly normal smooth rational surface S of degree 11 and sectional genus 8 in the projective fivespace. Surfaces satisfying these numerical invariants are special, in the sense that $h^1(\mathscr{O}_S(1))>0$. Our…

Let $(X,D)$ be a log smooth pair of dimension $n$, where $D$ is a reduced effective divisor such that the log canonical divisor $K_X + D$ is pseudo-effective. Let $G$ be a connected algebraic subgroup of $\mathrm{Aut}(X,D)$. We show that…

In this expository article, we prove a birational classification of smooth projective models of surfaces with negative Kodaira dimension over $\mathbb{Z}$ and over more general rings of integers $\mathcal{O}_K$, depending on their…

Let $L$ be an ample line bundle over a smooth projective toric surface $X$. Then $L$ corresponds to a very ample lattice polytope $P$ that encodes many geometric properties of $L$. In this article, by studying $P$, we will give some…

Let $f:X@>>>\Bbb P^1$ be a fibered surface with fibers of genus g>1. If f is semistable and non isotrivial we prove that X of non negative Kodaira dimension implies that the number s of singular fibers is at least 5. Information about the…

Let $(X,D)$ be an open log del Pezzo surface of rank one, that is, $X$ is a normal projective surface of Picard rank one, the boundary $D$ is a reduced nonzero divisor on $X$, and the anti-log canonical divisor $-(K_X+D)$ is ample. We show…

We prove a logarithmic base change theorem for pushforwards of pluri-canonical bundles and use it to deduce that positivity properties of log canonical divisors descend via smooth projective morphisms. As an application, for a surjective…

The fundamental group of a smooth projective variety is fibered if it maps onto the fundamental group of smooth curve of genus 2 or more. The goal of this paper is to establish some strong restrictions on these groups, and in particular on…