29 citations · 99 across the 11 of their papers we have counts for
12 papers · 1 filter
On a combinatorial description of the Gorenstein index for varieties with torus action
Philipp Iber, Eva Reinert, Milena Wrobel
The anticanonical complex is a combinatorial tool that was invented to extend the features of the Fano polytope from toric geometry to wider classes of varieties. In this note we s…
On Degenerations of the Projective Plane
Jürgen Hausen, Katharina Király, Milena Wrobel
Complementing results of Hacking and Prokhorov, we determine in an explicit manner all log terminal, rational, degenerations of the projective plane that allow a non-trivial torus…
Smooth Fano intrinsic Grassmannians of type with Picard number two
Muhammad Imran Qureshi, Milena Wrobel
We introduce the notion of intrinsic Grassmannians which generalizes the well known weighted Grassmannians. An intrinsic Grassmannian is a normal projective variety whose Cox ring…
The anticanonical complex for non-degenerate toric complete intersections
Juergen Hausen, Christian Mauz, Milena Wrobel
The anticanonical complex generalizes the Fano polytope from toric geometry and has been used to study Fano varieties with torus action so far. We work out the case of complete int…
On Fano threefolds with -action
Christoff Hische, Milena Wrobel
We study three-dimensional Fano varieties with -action. Complementing recent results [13], we give classification results in the canonical case, where the maximal orb…
Towards classifying toric degenerations of cubic surfaces
Maria Donten-Bury, Paul Görlach, Milena Wrobel
We investigate the class of degenerations of smooth cubic surfaces which are obtained from degenerating their Cox rings to toric algebras. More precisely, we work in the spirit of…
On the anticanonical complex
Christoff Hische, Milena Wrobel
The anticanonical complex has been introduced as a natural generalization of the toric Fano polytope and so far has been succesfully used for the study of varieties with a torus ac…
Divisor class groups of rational trinomial varieties
Milena Wrobel
We give an explicit description of the divisor class groups of rational trinomial varieties. As an application, we relate the iteration of Cox rings of any rational variety with to…
On torus actions of higher complexity
Juergen Hausen, Christoff Hische, Milena Wrobel
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit…
On iteration of Cox rings
Juergen Hausen, Milena Wrobel
We characterize all varieties with a torus action of complexity one that admit iteration of Cox rings.
Log terminal singularities, platonic tuples and iteration of Cox rings
Ivan Arzhantsev, Lukas Braun, Juergen Hausen +1
Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived…
Non-complete rational T-varieties of complexity one
Juergen Hausen, Milena Wrobel
We consider rational varieties with a torus action of complexity one and extend the combinatorial approach via the Cox ring developed for the complete case in earlier work to the n…