37 citations · 164 across the 30 of their papers we have counts for
5 papers · 1 filter
Enumerative geometry of elliptic curves on toric surfaces
Yoav Len, Dhruv Ranganathan
We establish the equality of classical and tropical curve counts for elliptic curves on toric surfaces with fixed -invariant, refining results of Mikhalkin and Nishinou--Siebert…
Degenerations of toric varieties over valuation rings
Tyler Foster, Dhruv Ranganathan
We develop a theory of multi-stage degenerations of toric varieties over finite rank valuation rings, extending the Mumford--Gubler theory in rank one. Such degenerations are const…
Skeletons of stable maps I: Rational curves in toric varieties
Dhruv Ranganathan
We study the Berkovich analytification of the space of genus logarithmic stable maps to a toric variety and present applications to both algebraic and tropical geometry. On…
Superabundant curves and the Artin fan
Dhruv Ranganathan
We prove that every balanced 1-dimensional polyhedral complex arises as the tropicalization of a smooth curve over a non-Archimedean field mapping to a toric Artin fan, namely the…
Hahn analytification and connectivity of higher rank tropical varieties
Tyler Foster, Dhruv Ranganathan
We show that the tropicalization of a connected variety over a higher rank valued field is a path connected topological space. This establishes an affirmative answer to a question…