相关论文: Arbitrarily large Galois orbits of non-homeomorphi…

We provide an infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group $SL_2(7)$. To my knowledge, this is the first instance of infinitely many such realizations for a perfect group which is…

For every $p\geq 2$ we show that each finite $p$-group with an unmixed Beauville structure is part of a surjective infinite projective system of finite $p$-groups with compatible unmixed Beauville structures. This leads to the new notion of…

In this note we construct an unlimited family of irregular algebraic surfaces of general type with canonical map of degree $ 8 $, irregularity $ 1 $ and arbitrarily large geometric genus such that the image of the canonical map is not a…

We consider the quotient X of bi-elliptic surface by a finite automorphism group. If X is smooth, then it is a bi-elliptic surface or ruled surface with irregularity one. As a corollary any bi-elliptic surface cannot be Galois covering of…

Strongly bounded groups are those groups for which every action by isometries on a metric space has orbits of finite diameter. Many groups have been shown to have this property, and all the known infinite examples so far have cardinality at…

We establish non-unirational versions of Hilbert Irreducibility for all Hilbert modular surfaces which are of K3 type. As an application we prove new instances of the regular Inverse Galois Problem for the simple groups…

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.

We construct first examples of discrete geometrically finite subgroups of PU(2,1) which contain parabolic elements, and are isomorphic to surface groups.

Let $p$ be an odd prime, and let $k$ be an arbitrary field of characteristic not $p$. In this article we determine the obstructions for the realizability as Galois groups over $k$ of all groups of orders $p^5$ and $p^6$, that have an…

We show that the Galois group $Gal(\bar{\Q} /\Q)$ operates faithfully on the set of connected components of the moduli spaces of surfaces of general type, and also that for each element $\sigma \in Gal(\bar{\Q} /\Q)$ different from the…

Chapters : Old and new inequalities; Surfaces with $\chi=1$ and the bicanonical map; Surfaces with $p_g=4$; Surfaces isogeneous to a product, Beauville surfaces and the absolute Galois group;Lefschetz pencils and braid monodromies;DEF, DIFF…

We construct examples of algebraic surfaces with interesting fundamental groups.

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

The automorphism group of the Galois covering induced by a pluri-canonical generic covering of a projective space is investigated. It is shown that by means of such coverings one obtains, in dimensions one and two, serieses of specific…

We classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the Picard group is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

Using Galois representations attached to elliptic curves, we construct Galois extensions of $\mathbb{Q}$ with group $GL_2(p)$ in which all decomposition groups are cyclic. This is the first such realization for all primes $p$.

We study Glois embeddings of K3 surfaces in the case where the Galois groups are abelian. We show several properties of K3 surfaces concerning the Galois embeddings. In particular, if the Galois group G is abelian, then G is isomorphic to…

We obtain simple generating sets for various mapping class groups of a nonorientable surface with punctures and/or boundary. We also compute the abelianizations of these mapping class groups.

This paper shows that the automorphism group of a Beauville surface is a finite solvable group, and describes its possible structure. It relies on results of Singerman on triangle group inclusions, and of Lucchini on generators for special…