Related papers: Pluripotential theory on algebraic curves

There is a natural pluripotential-theoretic extremal function V_{K,Q} associated to a closed subset K of C^m and a real-valued, continuous function Q on K. We define random polynomials H_n whose coefficients with respect to a related…

We develop analogues for Grauert tubes of real analytic Riemannian manifolds (M,g) of some basic notions of pluri-potential theory, such as the Siciak extremal function. The basic idea is to use analytic continuations of eigenfunctions in…

Let $A$ be a graded C*-algebra. We characterize Kasparov's K-theory group $\hat{K}_0(A)$ in terms of graded *-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded…

We obtain expressions for second kind integrals on non-hyperelliptic $(n,s)$-curves. Such a curve possesses a Weierstrass point at infinity which is a branch point where all sheets of the curve come together. The infinity serves as the…

This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the curve. In particular, we exploit the wild ramification to…

This article extends the study of cyclic ramified covers of the projective line defined by Kummer equations. We consider the most general case of such covers, allowing arbitrary orders in the roots of the generating radicant. The primary…

We consider orthogonal polynomials on the unit circle associated with certain semi-classical weight functions. This means that the Pearson-type differential equations satisfied by these weight functions involve two polynomials of degree at…

The Chebyshev polynomials are utilized in this study to define the subclass of the bi-univalent function. Also, Chebyshev polynomial bounds and Fekete-Szego inequalities for functions defined in the classes are established.

For a large class of word hyperbolic groups G the cross product C^*-algebra arising from the action of G on its Gromov boundary is shown to satisfy Poincare duality in K-theory. This class strictly contains fundamental groups of compact,…

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve $y^4 = x^5 + \lambda_4x^4 + \lambda_3x^3 + \lambda_2x^2 + \lambda_1x + \lambda_0$. We construct Abelian…

I discuss particular solutions of the integrable systems, starting from well-known dispersionless KdV and Toda hierarchies, which define in most straightforward way the generating functions for the Gromov-Witten classes in terms of the…

A kind of motivic stable homotopy theory of algebras is developed. Explicit fibrant replacements for the $S^1$-spectrum and $(S^1,\mathbb G)$-bispectrum of an algebra are constructed. As an application, unstable, Morita stable and stable…

We calculate explicit formulas for the general equivariant Bondal-Orlov functors on the localized K-theory groups for a crepant birational transformation of toric DM stacks. We recall some facts that the Bondal-Orlov functors give…

Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on $C^2$ smooth Jordan curves and arcs. The results are formulated in terms of the normal derivatives of certain Green's functions with…

Let $K$ be an algebraically closed field of characteristic different from 2, $g$ a positive integer, $f(x)$ a degree $(2g+1)$ polynomial with coefficients in $K$ and without multiple roots, $C: y^2=f(x)$ the corresponding genus $g$…

We calculate the algebraic $K$-theory of the coordinate ring of a planar cuspidal curve over a regular $\mathbb{F}_p$-algebra, thereby verifying a conjecture due to Hesselholt. In the course of the proof we compute the Picard group of the…

This is the second part of our work on Zariski decomposition structures, where we compare two different volume type functions for curve classes. The first function is the polar transform of the volume for ample divisor classes. The second…

We discuss the Siciak-Zaharjuta extremal function of pluripotential theory for the unit ball in C^d for spaces of polynomials with the notion of degree determined by a convex body P. We then use it to analyze the approximation properties of…

We extend unbounded Kasparov theory to encompass conformal group and quantum group equivariance. This new framework allows us to treat conformal actions on both manifolds and noncommutative spaces. As examples, we present unbounded…

In this survey article we review Kac-Moody and Heisenberg algebra actions on the categories $\mathcal{O}$ of the rational Cherednik algebras associated to groups $G(\ell,1,n)$. Using these actions we solve basic representation theoretic…