Related papers: Quartic surfaces with icosahedral symmetry

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…

It is known that an automorphism group of a K3 surface with Picard number two is either infinite cyclic group or infinite dihedral group if it is infinite. In this paper, we study the generators of an automorphism group. We use the…

We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.

Koras-Russell threefolds are certain smooth contractible complex hypersurfaces in affine complex four-space which are not algebraically isomorphic to affine three-space. One of the important examples is the cubic Russell threefold, defined…

We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry…

A group-theoretical approach to the construction of quasiperiodic tilings of a Euclidean plane, possessing five-fold symmetry, is applied. Of the infinitely many of variants of quasiperiodic partitions of the plane, possessing the dihedral…

In the present paper, we revisit the geometry of smooth plane quartics and their bitangents from several perspectives. First, we study in detail the weak combinatorics of arrangements of bitangents associated with highly symmetric quartic…

This paper is about the family of smooth quartic surfaces $X \subset \mathbb{P}^3$ that are invariant under the Heisenberg group $H_{2,2}$. For a very general such surface $X$, we show that the Picard number of $X$ is 16 and determine its…

In this paper, we study the Picard group of the moduli space of semistable sheaves on a smooth quadric surface. We polarize the surface by an ample divisor close to the anticanonical class. We focus especially on moduli spaces of sheaves of…

A few facts concerning the phrase "the automorphism groups become larger at special points of the moduli of K3 surfaces" are presented. It is also shown that the automorphism groups are of infinite order over a dense subset in any…

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

We consider the action of the group $\mathrm{PGL}_4(K)$ on the smooth cubic surfaces of $\mathbb{P}^3_K$ ($K$ an algebraically closed field of characteristic zero). We classify, in an explicit way, all the smooth cubic surfaces with non…

Let $N$ be a connected nonorientable surface of genus $g$ with $n$ punctures. Suppose that $g$ is odd and $g+n \geqslant 6$. We prove that the automorphism group of the complex of curves of $N$ is isomorphic to the mapping class group…

We complete the classification of automorphism groups of del Pezzo surfaces over algebraically closed fields of odd positive characteristic.

Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial…

We show that the automorphism group of the complex of pants decompositions for a surface is isomorphic to the mapping class group for that surface.

Let $S$ be the (minimal) Enriques surface obtained from the symmetric quartic surface $(\sum_{i<j}x_ix_j)^2=kx_1x_2x_3x_4$ in $\mathbb{P}^3$ with $k\neq 0,4,36$, by taking quotient of the Cremona action $(x_i) \mapsto (1/x_i)$. The…

Kummer surfaces are special quartic surfaces that admit $16$ nodes. The automorphisms of K3 Kummer surfaces are rich and complicated. Based on the results of Keum and Kond\=o, and as a continuation of the recent result by He and Yang, we…

We prove that there is a smooth quartic K3 surface automorphism that is not derived from the Cremona transformation of the ambient three-dimensional projective space. This gives a negative answer to a question of Professor Marat Giz.atullin

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 $\mathbb{P}^3$.