Add to ORKGWe study a relationship between rational proper maps of balls in different dimensions and strictly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putting the unique critical point of this exhaustion function at the origin leads to a normal form for rational proper maps of balls. The normal form of the map, which is up to composition with unitaries, takes the origin to the origin, and it normalizes the denominator by eliminating the linear terms and diagonalizing the quadratic part. The singular values of the quadratic part of the denominator are spherical invariants of the map. When these singular values are positive and distinct, the normal form is determined up to a finite subgroup of the unitary group. We al...
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools f...
The exponential function maps the imaginary axis to the unit circle and, for many applications, this...
We extend the construction of the normal cone of a closed embedding of schemes to any locally of fin...
In this dissertation, we study how rigidity properties of proper holomorphic mappings from complex b...
Given a rational dominant map $\phi: Y \dashrightarrow X$ between two generic hypersurfaces $Y,X \su...
As models of strictly pseudoconvex domains, we consider holomorphic functions on the unit ball $\bal...
A holomorphic mapping f from a bounded domain D in $\doubc\sp{n}$ to a bounded domain $\Omega$ in $\...
A holomorphic mapping f from a bounded domain D in $\doubc\sp{n}$ to a bounded domain $\Omega$ in $\...
In this dissertation, the proper rational holomorphic maps from n-ball into (3n-2)-ball have been st...
Associated to any divisor in the Chow ring of a simplicial tropical fan, we construct a family of po...
We show that the totally nonnegative part of a partial flag variety $G/P$ (in the sense of Lusztig) ...
We show that the only $\psi$-Dirichlet numbers in a function field over a finite field are rational ...
AbstractWe classify up to conjugation with automorphisms the linear fractional self-maps of the unit...
We prove a generalisation of Rudin’s theorem on proper holomorphic maps from the unit ball to the ca...
We prove a generalisation of Rudin’s theorem on proper holomorphic maps from the unit ball to the ca...
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools f...
The exponential function maps the imaginary axis to the unit circle and, for many applications, this...
We extend the construction of the normal cone of a closed embedding of schemes to any locally of fin...
In this dissertation, we study how rigidity properties of proper holomorphic mappings from complex b...
Given a rational dominant map $\phi: Y \dashrightarrow X$ between two generic hypersurfaces $Y,X \su...
As models of strictly pseudoconvex domains, we consider holomorphic functions on the unit ball $\bal...
A holomorphic mapping f from a bounded domain D in $\doubc\sp{n}$ to a bounded domain $\Omega$ in $\...
A holomorphic mapping f from a bounded domain D in $\doubc\sp{n}$ to a bounded domain $\Omega$ in $\...
In this dissertation, the proper rational holomorphic maps from n-ball into (3n-2)-ball have been st...
Associated to any divisor in the Chow ring of a simplicial tropical fan, we construct a family of po...
We show that the totally nonnegative part of a partial flag variety $G/P$ (in the sense of Lusztig) ...
We show that the only $\psi$-Dirichlet numbers in a function field over a finite field are rational ...
AbstractWe classify up to conjugation with automorphisms the linear fractional self-maps of the unit...
We prove a generalisation of Rudin’s theorem on proper holomorphic maps from the unit ball to the ca...
We prove a generalisation of Rudin’s theorem on proper holomorphic maps from the unit ball to the ca...
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools f...
The exponential function maps the imaginary axis to the unit circle and, for many applications, this...
We extend the construction of the normal cone of a closed embedding of schemes to any locally of fin...