Related papers: Rigid Flat Webs on the Projective Plane

We show that, for any fixed weight, there is a natural system of Hodge sheaves, whose Higgs field has no poles, arising from a flat projective family of varieties parametrized by a regular complex base scheme, extending the analogous…

We provide a geometric explanation for the existence of magnification relations for the A, D, E family of caustic singularities, which were established in recent work. In particular, it was shown that for families of general mappings…

We deduce general expressions for the line element of universe models with negative and vanishing spatial curvature described by conformally flat spacetime coordinates. The empty Milne universe model and models with dust, radiation and…

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

We show that the isolated invariant branches globalize to algebraic curves, when we consider weak toric type complex hyperbolic foliations on projective toric ambient surfaces. To do it, we pass through a characterization of weak toric type…

We find a new family of non-separable coordinate transformations bringing the FRW metrics into the manifestly conformally flat form. Our results are simple and complete, while our derivation is quite explicit. We also calculate all the FRW…

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties…

This paper develops projection-free algorithms for online convex optimization with stochastic constraints. We design an online primal-dual projection-free framework that can take any projection-free algorithms developed for online convex…

We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry…

We give restrictions on the existence of families of curves on smooth projective surfaces $S$ of nonnegative Kodaira dimension all having constant geometric genus $g \geq 2$ and hyperelliptic normalizations. In particular, we prove a…

We study Hodge loci as leaf schemes of foliations. The main ingredient is the Gauss-Manin connection matrix of families of projective varieties. We also aim to investigate a conjecture on the ring of definition of leaf schemes and its…

It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…

We show that an odd dimensional closed manifold with positive curvature cannot contain an incompressible real projective plane in the sense that there is no map of the projective plane into the manifold which is nontrivial on both first and…

We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle…

In this paper, we discuss filamentations on oriented chord diagrams. When a filamentation cannot be realized on an oriented chord diagram, then the corresponding flat virtual knot is non-trivial. If a flat knot diagram is non-trivial, then…

We consider conformally flat hypersurfaces in four dimensional space forms with their associated Guichard nets and Lam\'e's system of equations. We show that the symmetry group of the Lam\'e's system, satisfying Guichard condition, is given…

We prove a generic flatness result for the cohomology of thickenings of a projective scheme that is smooth over a Noetherian domain containing a field of characteristic zero. Our study is motivated, in part, by a classical question in…

We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order…

We show that projective structures with torsion are described in terms of affine connections in a parallel way as in the torsion-free case which is done by Kobayashi and Nagano. For this, we make use of a bundle of formal frames, which is a…

In a fibre bundle, natural derivatives of a section are defined as tangent vector fields on the image of a section of the fibre bundle. A local extension to vector fields in the tangent bundle leads to a direct proof of the formula…