Related papers: Explicit Schoen surfaces

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…

In this paper we study minimal algebraic surfaces with $p_g=q=1,K^2=4$ and nonhyperelliptic Albanese fibrations of genus 4. We construct for the first time a family of such surfaces as complete intersections of type $(2,3)$ in a…

In this paper, we classified the surfaces whose canonical maps are abelian covers over $\mathbb{P}^2$. Moveover, we construct a new Campedelli surface with fundamental group $\mathbb{Z}_2^{\oplus 3}$ and give defining equations for…

We study infinitesimal deformations of complete hyperbolic surfaces with boundary and with ideal vertices, possibly decorated with horoballs. ``Admissible'' deformations are the ones that pull all horoballs apart; they form a convex cone of…

Using the invariant algebra of the reflection group denoted by $G\_{32}$ in Shephard-Todd classification, we construct three irreducible surfaces in $P^3$ with many singularities: one of them has degree $24$ and contains $1440$ quotient…

We construct algebraic surfaces with a large number of type A singularities. Bivariate polynomials presented in previous works for the construction of nodal surfaces and certain families of Belyi polynomials are used. In some cases explicit…

We compute the automorphisms groups of all numerical Godeaux surfaces, i.e. minimal smooth surfaces of general type with K^2 = 1 and p_g = 0, with torsion of the Picard group of order \nu equals 3, 4, or 5. We present explicit…

Let X be the base locus of a linear system W of k quadrics. Let also S be the intersection of W with the discriminant hypersurface in the space of all homogeneous polynomials of degree two. We prove a formula relating the topology of X with…

We give an exponential upper and a quadratic lower bound on the number of pairwise non-isotopic simple closed curves can be placed on a closed surface of genus g such that any two of the curves intersects at most once. Although the gap is…

We construct a new family of minimal surfaces of general type with $p_g=q=2$ and $K^2=6$, whose Albanese map is a quadruple cover of an abelian surface with polarization of type $(1,3)$. We also show that this family provides an irreducible…

We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not…

In this paper we determine which automorphisms of general smooth quartic surfaces $S\subset \mathbb{P}^3$ of Picard rank $2$ are restrictions of Cremona transformations of $\mathbb{P}^3$.

We give a defining equation of a complex smooth quartic surface containing 56 lines, and investigate its reductions to positive characteristics. This surface is isomorphic to the complex Fermat quartic surface, which contains only 48 lines.…

We construct one dimensional families of Abelian surfaces with quaternionic multiplication which also have an automorphism of order three or four. Using Barth's description of the moduli space of (2,4)-polarized Abelian surfaces, we find…

In this, the last of three papers about $C_2$-equivariant complex quadrics, we complete the calculation of the equivariant ordinary cohomology of smooth symmetric quadrics in the cases where the fixed sets have more than two components.…

We give a full classification of higher order parallel surfaces in three-dimensional homogeneous spaces with four-dimensional isometry group, i.e. in the so-called Bianchi-Cartan-Vranceanu family. This gives a positive answer to a…

In this paper I investigate minimal surfaces of general type with p_g=5, q=0 for which the 1-canonical map is a birational morphism onto a surface in P^4 (so called canonical surfaces in P^4) via a structure theorem for the Hilbert…

We prove the existence of $(20-2K^2)$-dimensional families of simply-connected surfaces with ample canonical class, $p_g=1$, and $1 \leq K^2 \leq 9$, and we study the relation with configurations of rational curves in K3 surfaces via…

A recent result shows that a general smooth plane quartic can be recovered from its 24 inflection lines and a single inflection point. Nevertheless, the question whether or not a smooth plane curve of degree at least 4 is determined by its…

Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthogonal surfaces in one or two dimensions are rather trivial…