Related papers: The Higher Connectivity of Intersections of Real Q…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
In this short note we observe that the higher topological complexity of an iterated connected sum of real projective spaces is maximal possible. Unlike the case of regular TC, the result is accessible through easy mod 2 zero-divisor…
A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
The notion of non-projectible contact forms on a given compact manifold $M$ is introduced by the first-named author in [Ohb], the set of which he also shows is a residual subset of the set of (coorientable) contact forms, both in the case…
We study real nonsingular projective cubic fourfolds up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in the…
Let $X$ be a compact Riemann surface. A quadratic pair on $X$ consists of a holomorphic vector bundle with a quadratic form which takes values in fixed line bundle. We show that the moduli spaces of quadratic pairs of rank 2 are connected…
We study some properties of an embedded variety covered by lines and give a numerical criterion ensuring the existence of a singular conic through two of its general points. We show that our criterion is sharp. Conic-connected, covered by…
This paper proves that every projective toric variety is the fine moduli space for stable representations of an appropriate bound quiver. To accomplish this, we study the quiver $Q$ with relations $R$ corresponding to the finite-dimensional…
It is shown that for non-hyperbolic real quadratic polynomials topological and quasisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that…
We describe a family of hyperbolic knots whose character variety contain exactly two distinct components of characters of irreducible representations. The intersection points between the components carry rich topological information. In…
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 describe a natural open stratum in the moduli space of smooth real pointed quartic curves in the projective plane. This stratum consists of real isomorphism classes of pairs $(C, p)$ with $p$ a real point on the curve $C$ such that the…
A connected topological space is said to be widely-connected if each of its non-degenerate connected subsets is dense in the entire space. The object of this paper is the construction of widely-connected subsets of the plane. We give a…
We relate the geometry of curves to the notion of hyperbolicity in real algebraic geometry. A hyperbolic variety is a real algebraic variety that (in particular) admits a real fibered morphism to a projective space whose dimension is equal…
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…
We obtain criteria for detecting complete intersections in projective varieties. Motivated by a conjecture of Hartshorne concerning subvarieties of projective spaces, we investigate situations when two-codimensional smooth subvarieties of…
We show that the variable cohomology of a general complete intersection of quadrics can be identified with the intersection cohomology of a double covering. As a consequence, we show that the middle cohomology of a general complete…
The topological complexity ${\sf TC}(X)$ is a homotopy invariant of a topological space $X$, motivated by robotics, and providing a measure of the navigational complexity of $X$. The topological complexity of a connected sum of real…
The first examples of complete projective connections are uncovered: normal projective connections on surfaces whose geodesics are all closed and embedded are complete, as are normal projective connections induced from complete affine…
A periodic weave is the lift of a particular link embedded in a thickened surface to the universal cover. Its components are infinite unknotted simple open curves that can be partitioned in at least two distinct sets of threads. The…