相关论文: On non-projective normal surfaces

The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.

Regular algebraic surfaces isogenous to a higher product of curves can be obtained from finite groups with ramification structures. We find unmixed ramification structures for finite groups constructed as p-quotients of particular infinite…

We provide examples of finite non-abelian groups acting on non-trivial Severi-Brauer surfaces.

We investigate the projective normality of smooth, linearly normal surfaces of degree 9. All non projectively normal surfaces which are not scrolls over a curve are classified. Results on the projective normality of surface scrolls are also…

Let A=k+A_1+A_2.... be a connected graded, noetherian k-algebra that is generated in degree one over an algebraically closed field k. Suppose that the graded quotient ring Q(A) has the form Q(A)=k(Y)[t,t^{-1},sigma], where sigma is an…

We study the birational properties of hypersurfaces in products of projective spaces. In the case of hypersurfaces in P^m x P^n, we describe their nef, movable and effective cones and determine when they are Mori dream spaces. Using these…

We study the nef cones of complex smooth projective surfaces and give a sufficient criterion for them to be non-polyhedral. We use this to show that the nef cone of C x C, where C is a complex smooth projective curve of genus at least 2, is…

We will show that there is a smooth complex projective surface, birational to some Enriques surface, such that the automorphism group is discrete but not finitely generated.

We give a natural parameterization of the N\'eron-Severi group of a product $A = E\times E'$ of two elliptic curves in terms of quadratic forms. As an application, we determine (in the non-CM case) whether $A$ contains a smooth curve of any…

We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.

Let $p$ and $q$ be odd prime numbers. In this paper we study non-abelian pq-fold regular covers of the projective line, determine algebraic models for some special cases and provide a general isogeny decomposition of the corresponding…

We give a version of the Artin-Tate formula for surfaces over finite fields not assuming Tate's conjecture. It gives an equality between terms related to the Brauer group on the one hand and terms related to the Neron-Severi group on the…

Our main result is the following: let X be a normal affine toric surface without torus factor. Then there exists a non-normal affine toric surface X' with automorphism group isomorphic to the automorphism group of X if and only if X is…

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and…

We work out properties of smooth projective varieties over a (not necessarily algebraically closed) field that admit collections of objects in the bounded derived category of coherent sheaves that are either full exceptional, or numerically…

In this paper, we study non-planar degeneracies with cylindrical configurations. They could be constructed by the product $\mathbb{CP}^1 \times T$ of the projective plane and a complex torus with embedding $(m,n)$. We prove that their…

We present a complete classification of complex projective surfaces $X$ with nontrivial self-maps (i.e. surjective morphisms $f:X\rightarrow X$ which are not isomorphisms) of any given degree. The starting point of our classification are…

We study the higher Chow groups $CH^2(X,1)$ and $CH^3(X,2)$ of smooth, projective algebraic surfaces over a field of char 0. We develop a theoretical framework to study them by using so-called higher normal functions and higher…

Self-rational maps of generic algebraic K3 surfaces are conjectured to be trivial. We relate this conjecture to a conjecture concerning the irreducibility of the universal Severi varieties parametrizing nodal curves of given genus and…

We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the…