$H$-cones and potential theory

Cones in Homotopy Probability Theory

This note defines cones in homotopy probability theory and demonstrates that a cone over a space is a reasonable replacement for the space. The homotopy Gaussian distribution in one variable is revisited as a cone on the ordinary Gaussian.

Nonsymmetric potential-reduction methods for general cones

In this paper we propose two new nonsymmetric primal-dual potential-reduction methods for conic problems. The methods are based on the primal-dual lifting [5]. This procedure allows to construct a strictly feasible primal-dual pair related by an exact scaling relation even if the cones are not symmetric. It is important that all necessary elements of our methods can be obtained from the standar...

K-theory of Cones of Smooth Varieties

Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve then we calculate K0(R) and K1(R), and prove that K−1(R) = ⊕H(C,O(n)). The formula for K0(R) involves the Zariski cohomology of twisted Kähler differentials on the va...

Turing cones and set theory of the reals

Balanced Normal Cones and Fulton-macpherson’s Intersection Theory

Let X be a subscheme of a reduced scheme Y. Then Y has a flat degeneration to the normal cone CXY of X, and this degeneration plays a key step in Fulton and MacPherson’s “basic construction” in intersection theory. The intersection product has a canonical refinement as a sum over the components of CXY, for X and Y depending on the given intersection problem. The cone CXY is usually not reduced,...