36 citations · 130 across the 18 of their papers we have counts for
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math.AC2015★ 2 cited
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…
math.AG2015★ 8 cited
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…
math.AG2015★ 7 cited
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…