This article is an introduction to matroid theory aimed at algebraic geometers. Matroids are
combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all …

The goal of this paper is to propose a theory of mirror symmetry for varieties of general type.
Using Landau–Ginzburg mirrors as motivation, we describe the mirror of a hypersurface of …

Let D be a divisor with simple normal crossings on an algebraic variety. The dual complex
(D) is a triangulated topological space, or-complex, whose k-dimensional simplices …

We propose a geometric interpretation of Block and Göttsche's refined tropical curve
counting invariants in terms of virtual χ− y specializations of motivic measures of …

Monodromy Filtrations and the Topology of Tropical Varieties Page 1 Canad. J. Math. Vol. 64
(4), 2012 pp. 845–868 http://dx.doi.org/10.4153/CJM-2011-067-9 c Canadian Mathematical …

This note surveys basic topological properties of nonarchimedean analytic spaces, in the
sense of Berkovich, including the recent tameness results of Hrushovski and Loeser. We …

This paper generalises the homeomorphism theorem behind Viro's combinatorial
patchworking of hypersurfaces in toric varieties to arbitrary codimension using tropical …

EULER CHARACTERISTIC AND SIGNATURE OF REAL SEMI-STABLE DEGENERATIONS
Page 1 J. Inst. Math. Jussieu (2023), 22(5), 2447–2454 doi:10.1017/S1474748022000056 © …

Given a family X of complex varieties degenerating over a punctured disk, one is interested
in computing related invariants called the motivic nearby fiber and the refined limit mixed …

We introduce tropical complexes, as an enrichment of the dual complex of a degeneration
with additional data from non-transverse intersection numbers. We define cycles, divisors …