Related papers: Rigid Flat Webs on the Projective Plane

We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional…

It is known that for any full rational conformal field theory, the correlation functions that are obtained by the TFT construction satisfy all locality, modular invariance and factorization conditions, and that there is a small set of…

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…

In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-invariant is defined and described in terms…

In this article, we introduce a new approach to show the existence and smoothing of simple normal crossing varieties in a given projective space. Our approach relates the above to the existence of nowhere reduced schemes called ribbons and…

We continue our work on the model theory of free lattices, solving two of the main open problems from our first paper on the subject. Our main result is that the universal (existential) theory of infinite free lattices is decidable. Our…

We study geometric properties of certain obstructed equisingular families of projective hypersurfaces with emphasis on smoothness, reducibility, being reduced, and having expected dimension. In the case of minimal obstructness, we give a…

Let K be an algebraically closed field endowed with a complete non-archimedean norm. Let f:Y -> X be a map of K-affinoid varieties. We prove that for each point x in X, either f is flat at x, or there exists, at least locally around x, a…

This work presents a generalization of derived blow-ups and of the derived deformation to the normal bundle from derived algebraic geometry to any geometric context. The latter is our proposed globalization of a derived algebraic context,…

In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $\Bbb R^2.$ The classification gives…

We define and study jets of flat partial connections in the setting of smooth foliations and flat partial connections on locally free sheaves. In the case of codimension one foliations, we apply this definition to characterize transversely…

We prove that a generic holomorphic foliation on a weighted projective plane has no algebraic solutions when the degree is big enough. We also prove an analogous result for foliations on Hirzebruch surfaces.

Let LG be an algebraic loop group associated to a reductive group G. A fundamental stratum is a triple consisting of a point x in the Bruhat-Tits building of LG, a nonnegative real number r, and a character of the corresponding depth r…

The classical Pfaff-Darboux theorem, which provides local 'normal forms' for $1$-forms on manifolds, has applications in the theory of certain economic models [Chiappori P.-A., Ekeland I., Found. Trends Microecon. 5 (2009), 1-151]. However,…

A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as…

A very good cubic fourfold is a smooth cubic fourfold that does not contain a plane, a cubic scroll, or a hyperplane section with a corank 3 singularity. We prove that the normalization of the relative compactified Prym variety associated…

We prove flatness of complete Riemannian planes and cylinders without conjugate points under optimal conditions on the area growth.

Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field and let $X\to \mathrm{Spec} (A)$ be a resolution of singularity. We prove a theorem giving a condition under which the dimension of the…

For $G$ a split semi-simple group scheme and $P$ a principal $G$-bundle on a relative curve $X\to S$, we study a natural obstruction for the triviality of $P$ on the complement of a relatively ample Cartier divisor $D \subset X$. We show,…

In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…