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This note shows the compatibility of the differential geometric and the topological formulations of equivariant characteristic classes for a compact connected Lie group action.

This note contains some results related to the definitions of toroidal embeddings and toroidal morphisms over non-closed fields of characteristic zero.

This paper is devoted to a discussion of specific properties of invariants in the theory of forms.

We describe the topology of critical loci of coamoeba of generic affine planes in four-space.

The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described using polynomials in the coordinate ring, and we generalise…

This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.

We describe the set of characteristic polynomials of abelian varieties of dimension 4 over finite fields.

We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.

We describe the set of characteristic polynomials of abelian varieties of dimension 3 over finite fields.

We describe a singular variety associated to the smallest degree Pinchuk map and calculate its intersection homology. The result describes the geometry at infinity of the Pinchuk's map.

This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…

We introduce and study on examples a notion of the Artin shape for a motive related to a projective homogenous variety. We apply it to the problem of finding the complete motivic decomposition of the variety. Our examples cover unitary…

Generalizing Howie and Greene's characterization of alternating knots, we give a topological characterization of almost alternating knots.

We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig's label and in terms of…

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…

We prove some fundamental structural results for spherical varieties in arbitrary characteristic. In particular, we study Luna's two types of localization and use it to analyze spherical roots, colors and their interrelation. At the end, we…

In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.

We define a topological invariant of complex projective plane curves. As an application, we present new examples of arithmetic Zariski pairs.

Using factorizable Hopf algebras, we construct modular invariant partition functions of charge conjugation, or Cardy, type as characters of coends in categories that share essential features with the ones appearing in logarithmic CFT. The…

For a variety with a finitely generated total coordinate ring, we describe basic geometric properties in terms of certain combinatorial structures living in its divisor class group. For example, we describe the singularities, we calculate…