Related papers: Smooth factorial affine surfaces of logarithmic Ko…

A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the…

We consider singular Q-acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is C^1- or C*-ruled or the surface is up to isomorphism one of two…

Using the affine web category introduced in a prequel as a building block, we formulate a diagrammatic $\Bbbk$-linear monoidal category, the affine Schur category, for any commutative ring $\Bbbk$. We then formulate diagrammatic categories,…

A smooth, projective surface $S$ is called a $\emph{standard isotrivial fibration}$ if there exists a finite group $G$ which acts faithfully on two smooth projective curves $C$ and $F$ so that $S$ is isomorphic to the minimal…

In this paper, we study $\mathbb{A}^1$-equivalence classes of zero cycles on open complex algebraic surfaces. We prove the logarithmic version of Mumford's theorem on zero cycles and prove that log Bloch's conjecture holds for…

We give new contributions to the existence problem of canonical surfaces of high degree. We construct several families (indeed, connected components of the moduli space) of surfaces $S$ of general type with $p_g=5,6$ whose canonical map has…

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…

This paper classifies surfaces of general type $S$ with $p_g=q=1$ having an involution $i$ such that $S/i$ has non-negative Kodaira dimension and that the bicanonical map of $S$ factors through the double cover induced by $i.$ It is shown…

Let V be a smooth quasi-projective complex surface such that the three first logarithmic plurigenera are equal to 1 and the logarithmic irregularity is equal to 2. We prove that the quasi-Albanese morphism of V is birational and there…

In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our…

In this paper, we establish a criterion for an overconvergent isocrystal on a smooth variety over a field of characteristic $p>0$ to extend logarithmically to its smooth compactification whose complement is a strict normal crossing divisor.…

We construct a new family of minimal smooth surfaces of general type with K^2=7 and p_g= 0. We show that for a surface in this family, its canonical divisor is ample and its bicanonical morphism is birational. We prove that these surfaces…

A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in…

Let T -> S be a finite flat morphism of degree two between regular integral schemes of dimension at most two (and with 2 invertible), having regular branch divisor D. We establish a bijection between Azumaya quaternion algebras on T and…

A rational elliptic surface with section is a smooth, rational, complex, projective surface $\mathcal{X}$ that admits a relatively minimal fibration $f: \mathcal{X}\longrightarrow \bbP^1$ such that its general fibre is a smooth irreducible…

We construct algebraic families of exotic affine 3-spheres, that is, smooth affine threefolds diffeomorphic to a non-degenerate smooth complex affine quadric of dimension 3 but non algebraically isomorphic to it. We show in particular that…

We start to study the problem of classifying smooth proper varieties over a field k from the standpoint of A^1-homotopy theory. Motivated by the topological theory of surgery, we discuss the problem of classifying up to isomorphism all…

Let S be a closed surface of genus g >= 2 and z in S a marked point. We prove that the subgroup of the mapping class group Map(S,z) corresponding to the fundamental group pi_1(S,z) of the closed surface does not lift to the group of…

We prove that the first integral cohomology of pure mapping class groups of infinite type genus one surfaces is trivial. For genus zero surfaces we prove that not every homomorphism to $\mathbb{Z}$ factors through a sphere with finitely…

We prove several results in the theory of fusion categories using the product (norm) and sum (trace) of Galois conjugates of formal codegrees. First, we prove that finitely-many fusion categories exist up to equivalence whose global…