Related papers: Triangulations and Severi varieties

Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…

We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…

A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations of closed orientable surfaces. Those surfaces arise as the…

In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal…

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…

The complex Plateau problem is analogous, in a Hermitian complex manifold, to the classical Plateau problem in 3 dimensional real space: it is a geometrical problem of extension of a closed real manifold into a complex analytic subvariety,…

This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, inductive limit group, Zariski topology and the dimension of the…

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…

The main objects of the paper are $z$-oriented triangulations of connected closed $2$-dimensional surfaces. A $z$-orientation of a map is a minimal collection of zigzags which double covers the set of edges. We have two possibilities for an…

This paper begins the exploration of what we call measures of association between two irreducible complex projective varieties of the same dimension. The idea is to study from various points of view the minimal complexity of correspondences…

In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an…

We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the…

We present two versions of a method for generating all triangulations of any punctured surface in each of these two families: (1) triangulations with inner vertices of degree at least 4 and boundary vertices of degree at least 3 and (2)…

We outline the proof that non-triangulable manifolds exist in any dimension greater than four. The arguments involve homology cobordism invariants coming from the Pin(2) symmetry of the Seiberg-Witten equations. We also explore a related…

If the four triangular facets of a tetrahedron can be partitioned into pairs having the same area, then the triangles in each pair must be congruent to one another. A Heron-style formula is then derived for the volume of a tetrahedron…

R. Hartshorne conjectured and F. Zak proved that any n-dimensional smooth non-degenerate complex algebraic variety X in a m-dimensional projective space P satisfies Sec(X)=P if m<3n/2+2. In this article, I deal with the limiting case of…

In this survey article, we are interested on minimal triangulations of closed pl manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a…

Let ${\mathcal G}_k(V)$ be the $k$-Grassmannian of a vector space $V$ with $\dim V=n$. Given a hyperplane $H$ of ${\mathcal G}_k(V)$, we define in [I. Cardinali, L. Giuzzi, A. Pasini, A geometric approach to alternating $k$-linear forms, J.…

We prove the following generalization of Severi's Theorem: Let $X$ be a fixed complex variety. Then there exist, up to birational equivalence, only finitely many complex varieties $Y$ of general type of dimension at most three which admit a…