Related papers: Explicit Sarkisov program for regular surfaces ove…

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…

We consider generalizations of Szpiro's classical discriminant conjecture to hyperelliptic curves over a number field $K$, and to smooth, projective and geometrically connected curves $X$ over $K$ of genus at least one. The main results…

We prove the conjecture of Kac-Wakimoto on the rationality of exceptional W-algebras for the first non-trivial series, namely, for the Bershadsky-Polyakov vertex algebras $W_3^{(2)}$ at level $k=p/2-3$ with $p=3,5,7,...$. This gives new…

We investigate the universal Severi variety of rational curves on K3 surfaces, which parametrises irreducible rational curves in a fixed class on varying K3 surfaces of fixed genus. We investigate the conjecuted irreducibility of this space…

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…

We present a framework for constructing examples of smooth projective curves over number fields with explicitly given elements in their second K-group using elementary algebraic geometry. This leads to new examples for hyperelliptic curves…

We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational…

We show that plane Cremona groups over finite fields embed as dense subgroups into Neretin groups, i.e. groups of almost automorphisms of rooted trees. We also show that if the finite base field has even characteristic and contains at least…

We study toric varieties over an arbitrary field with an emphasis on toric surfaces in the Merkurjev-Panin motivic category of "K-motives". We explore the decomposition of certain toric varieties as K-motives into products of central simple…

Let $K=k(C)$ be the function field of a smooth projective curve $C$ over an infinite field $k$, let $X$ be a projective variety over $k$. We prove two results. First, we show with some conditions that a $K$-morphism $\phi: X_K \to X_K$ of…

We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…

We study Severi curves parametrizing rational bisections of elliptic fibrations associated to general pencils of plane cubics. Our main results show that these Severi curves are connected and reduced, and we give an upper bound on their…

We investigate the following conjecture: all compact non-K\"ahler complex surfaces admit birational structures. After Inoue-Kobayashi-Ochiai, the remaining cases to study are essentially surfaces in class VII_0^+. In case of Kato surfaces…

We prove that the torsion subgroup of the abelian fundamental group is finite for a regular geometrically integral projective variety over a local field. We also study the structure of $SK_1(X)$ for a regular projective variety $X$ over a…

Yanchevski\u{i} had asked whether conic bundle surfaces over $\mathbf{P}^1_k$ are unirational when $k$ is a finite field. We give a partial answer to his question by showing that for quasi-finite fields $k$ (e.g. finite fields) a regular…

We prove an extension of the Kato-Saito class field theory for smooth projective schemes over a finite field to schemes with singularities. As an application, we obtain Bloch's formula for the Chow groups of 0-cycles on such schemes. We…

We develop a mixed-characteristic version of the Mori-Mukai technique for producing rational curves on K3 surfaces. We reduce modulo p, produce rational curves on the resulting K3 surface over a finite field, and lift to characteristic…

We show that for each aspherical compact complex surface $X$ whose fundamental group $\pi$ fits into a short exact sequence $$ 1\to K \to \pi \to \pi_1(S) \to 1 $$ where $S$ is a compact hyperbolic Riemann surface and the group $K$ is…

This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic arithmetic surfaces and a formula for the "energy" of an isogeny between Riemann…

We define and study Gysin morphisms on mixed motives over a perfect field. Our construction extends the case of closed immersions, already known from results of Voevodsky, to arbitrary projective morphisms. We prove several classical…