4 papers
Weak Hodge Theorem on Piecewise-Algebraic Spaces
Takuya Murata, Aliakbar Hosseini
We prove a weak version of the classical Hodge theorem on piecewise-algebraic spaces, a class of spaces introduced by Kontsevich and Soibelman in [KS00]. Precisely, we first prove…
Maps to toric varieties, toric degenerations and integrable systems à la Harada--Kaveh
Takuya Murata, Lara Bossinger
Given a toric degeneration (a degeneration to a toric variety), over the complex numbers, we construct a surjective continuous map from a general fiber to the special fiber of the…
Generic tropical initial ideals of Cohen-Macaulay algebras
Kiumars Kaveh, Christopher Manon, Takuya Murata
We study the generic tropical initial ideals of a positively graded Cohen-Macaulay algebra over an algebraically closed field . Building on work of Römer and Schmit…
On degenerations of projective varieties to complexity-one T-varieties
Kiumars Kaveh, Christopher Manon, Takuya Murata
Let be a positively graded finitely generated -domain with Krull dimension . We show that there is a homogeneous valuation $\mathfrak{v}: R \setminus \{0\} \to…