24 citations · 93 across the 20 of their papers we have counts for
5 papers · 1 filter
Affine Spherical Mass and a Gaussian Kinematic Formula for Tropical Two-Fans
Nikita Kalinin
Let be an effective balanced rational two-dimensional fan in a rank-four lattice. We introduce an affine spherical mass \[ M_*(F)=\inf_{covol_g(N)=1}M_g(F) \] and prove the two…
Shrinking dynamic on multidimensional tropical series
Nikita Kalinin, Mikhail Shkolnikov
Let be a compact convex domain. An -tropical series is a nonnegative, concave, integral-slope, piecewise-affine function on that vanishes on $\partialΩ…
A guide to tropical modifications
Nikita Kalinin
This paper surveys {\it tropical modifications}, a notion that has become part of the folklore of tropical geometry. Tropical modifications are used in tropical intersection theory…
Tropical approach to Nagata's conjecture in positive characteristic
Nikita Kalinin
Suppose that there exists a hypersurface with the Newton polytope , which passes through a given set of subvarieties. Using tropical geometry, we associate a subset of to ea…
The Newton polygon of a planar singular curve and its subdivision
Nikita Kalinin
Let a planar algebraic curve be defined over a valuation field by an equation . Valuations of the coefficients of define a subdivision of the Newton polygon o…