26 citations · 68 across the 11 of their papers we have counts for
6 papers · 1 filter
Cayley-Bacharach Formulas
Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels
The Cayley-Bacharach Theorem states that all cubic curves through eight given points in the plane also pass through a unique ninth point. We write that point as an explicit rationa…
Bitangents of tropical plane quartic curves
Matt Baker, Yoav Len, Ralph Morrison +2
We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For…
Tropicalization of Del Pezzo Surfaces
Qingchun Ren, Kristin Shaw, Bernd Sturmfels
We determine the tropicalizations of very affine surfaces over a valued field that are obtained from del Pezzo surfaces of degree 5, 4 and 3 by removing their (-1)-curves. On these…
Algorithms for Mumford curves
Ralph Morrison, Qingchun Ren
Mumford showed that Schottky subgroups of give rise to certain curves, now called Mumford curves, over a non-Archimedean field K. Such curves are foundational to subject…
Tropicalization of classical moduli spaces
Qingchun Ren, Steven V Sam, Bernd Sturmfels
The image of the complement of a hyperplane arrangement under a monomial map can be tropicalized combinatorially using matroid theory. We apply this to classical moduli spaces that…
The Universal Kummer Threefold
Qingchun Ren, Steven V Sam, Gus Schrader +1
The universal Kummer threefold is a 9-dimensional variety that represents the total space of the 6-dimensional family of Kummer threefolds in 7-dimensional projective space. We com…