Related papers: Double Veronese cones with 28 nodes

We construct first examples of singular del Pezzo surfaces with Zariski dense exceptional sets in Manin's conjecture, varying in degrees $1, 2$ and $3$. The obstructions arise from accumulating quasi-\'etale covers. We classify all…

We study the abstract regular polyhedra with automorphism groups that act faithfully on their vertices, and show that each non-flat abstract regular polyhedron covers a "vertex-faithful" polyhedron with the same number of vertices. We then…

We revisit a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces, in which rational curves on the del Pezzo are related to ${1\over 2}$-BPS branes of the corresponding compactification. We argue that curves…

We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…

In this note we describe the image of $\PP^2$ in $ Gr(2, \CC^{4})$ under a morphism given by a rank two vector bundle on $\PP^2$ with Chern classes $(2,2).$

In this paper, we study tropicalisations of families of curves with a singularity in a fixed point. The tropicalisation of such a family is a linear tropical variety. We describe its maximal dimensional cones using results about linear…

We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair…

We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived…

For a double solid $V\to P_3(C)$ branched over a surface $B\subset P_3(C)$ with only ordinary nodes as singularities, we give a set of generators of the divisor class group $Pic(\tilde{V}})$ in terms of contact surfaces of $B$ with only…

We classify the self-dual (or holomorphic) vertex operator superalgebras of central charge 24, or in physics parlance the purely left-moving, fermionic 2-dimensional conformal field theories with just one primary field. There are exactly…

In this paper we address Fano foliations on complex projective varieties. These are foliations whose anti-canonical class is ample. We focus our attention on a special class of Fano foliations, namely del Pezzo foliations on complex…

We determine the versal deformation of cones, in the simplest case: cones over hyperelliptic curves of high degree. In particular, we show that for degree $4g+4$, the highest degree for which interesting deformations exist, the number of…

It is known that strongly involutive polyhedra are closely related to self-dual maps where the antipodal function acts as duality isomorphism. Such a family of polyhedra appears in different combinatorial, topological and geometric…

We introduce and study the notion of $G$-coregularity of algebraic varieties endowed with an action of a finite group $G$. We compute $G$-coregularity of smooth del Pezzo surfaces of degree at least 6, and give a characterization of groups…

Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called L\"uroth quartics. The locus of singular L\"uroth quartics has two irreducible components, both of codimension two in $\P^{14}$. We compute…

We describe relations between hyperbolic geometry and codimension two knots or, more exactly, between varieties of conjugacy classes of discrete faithful representations of the fundamental groups of hyperbolic n-manifolds M into…

The blow-up of the anticanonical base point on a del Pezzo surface $S$ of degree 1 gives rise to a rational elliptic surface $\mathscr{E}$ with only irreducible fibers. The sections of minimal height of $\mathscr{E}$ are in correspondence…

In this paper, we make use of the relations between the braid and mapping class groups of a compact, connected, non-orientable surface N without boundary and those of its orientable double covering S to study embeddings of these groups and…

We discuss the work of Corrado Segre on nodal cubic hypersurfaces with emphasis on the cases of 6-nodal and 10-nodal cubics. In particular, we discuss the Fano surface of lines and conic bundle structures on such threefolds. We review some…

We give an explicit construction for the $4$-dimensional family of Schoen surfaces by computing equations for their canonical images, which are $40$-nodal complete intersections of a quadric and the Igusa quartic in $\mathbb P^4$. We then…