Related papers: Partial Differential Chow Forms and a Type of Part…
We introduce the notion of a categorical valuative invariant of polyhedra or matroids, in which alternating sums of numerical invariants are replaced by split exact sequences in an additive category. We provide categorical lifts of a number…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization…
Recently, Chmutov introduced the partial duality of ribbon graphs, which can be regarded as a generalization of the classical Euler-Poincar\'e duality. The partial-dual genus polynomial $^\partial\varepsilon_G(z)$ is an enumeration of the…
Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or their multivariate generalizations. We determine the dimension, degree, singular locus and defining equations of these varieties. We explain how they play…
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
We introduce immanant varieties, associated to simple characters of a finite group. They include well-studied classes of varieties, as Segre embeddings, Grassmannians and certain other classes of Chow varieties. For a one-dimensional…
We obtain a precise relation between the Chern-Schwartz-MacPherson class of a subvariety of projective space and the Euler characteristics of its general linear sections. In the case of a hypersurface, this leads to simple proofs of…
We use the method of characteristic sets with respect to two term orderings to prove the existence and obtain a method of computation of a bivariate Kolchin-type dimension polynomial associated with a non-reflexive difference-differential…
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…
We use piecewise polynomials to define tropical cocycles generalising the well-known notion of tropical Cartier divisors to higher codimensions. Groups of cocycles are tropical analogues of Chow cohomology groups. We also introduce an…
We generalize the Chern class relation for the transversal intersection of two nonsingular varieties to a relation for possibly singular varieties, under a 'splayedness' assumption. The relation is shown to hold for both the…
We define an `enriched' notion of Chow groups for algebraic varieties, agreeing with the conventional notion for complete varieties, but enjoying a functorial push-forward for arbitrary maps. This tool allows us to glue…
Classically, the projective duality between joins of varieties and the intersections of varieties only holds in good cases. In this paper, we show that categorically, the duality between joins and intersections holds in the framework of…
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…
We introduce the notion of a partial dynamical symmetry for which a prescribed symmetry is neither exact nor completely broken. We survey the different types of partial dynamical symmetries and present empirical examples in each category.
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
We develop a cohomology theory of groups based on partial actions and explore its relation with the partial Schur multiplier as well as with cohomology of inverse semigroups.