36 citations · 130 across the 18 of their papers we have counts for
19 papers
Tropical floor plans and enumeration of complex and real multi-nodal surfaces
Hannah Markwig, Thomas Markwig, Kristin Shaw +1
The family of complex projective surfaces in projective three space of degree having precisely nodes as their only singularities has codimension in the linear system of…
Computing tropical varieties over fields with valuation
Thomas Markwig, Yue Ren
We show how tropical varieties of ideals I over a field K with non-trivial valuation can be traced back to tropical varieties of ideals in R[[t]][x] over some dense subring R in it…
Gröbner Fans of x-homogeneous Ideals in R[[t]][x]
Thomas Markwig, Yue Ren
We generalise the notion of Gröbner fan to ideals in R[[t]][x_1,...,x_n] for certain classes of coefficient rings R and give a constructive proof that the Gröbner fan is a rational…
Standard Bases in mixed Power Series and Polynomial Rings over Rings
Thomas Markwig, Yue Ren, Oliver Wienand
In this paper we study standard bases for submodules of a mixed power series and polynomial ring respectively of their localization with res…
Enumeration of Complex and Real Surfaces via Tropical Geometry
Hannah Markwig, Thomas Markwig, Eugenii Shustin
We prove a correspondence theorem for singular tropical surfaces in real three space, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize…
Tropical surface singularities
Hannah Markwig, Thomas Markwig, Eugenii Shustin
In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can…