8 citations · 18 across the 4 of their papers we have counts for
8 papers
Lefschetz decomposition and the cd-index of fans
Kalle Karu
The goal of this article is to give a Lefschetz type decomposition for the cd-index of a complete fan. To a complete simplicial fan one can associate a toric variety X, the even Be…
The cd-index of fans and lattices
Kalle Karu
The number of flags in a complete fan, or more generally in an Eulerian poset, is encoded in the cd-index. We prove non-negativity of the cd-index for complete fans, regular CW-sph…
Toric Residue Mirror Conjecture for Calabi-Yau complete intersections
Kalle Karu
We generalize the toric residue mirror conjecture of Batyrev and Materov to not necessarily reflexive polytopes. Using this generalization we prove the toric residue mirror conject…
Local Strong Factorization of birational maps
Kalle Karu
The strong factorization conjecture states that a proper birational map between smooth algebraic varieties over a field of characteristic zero can be factored as a sequence of smoo…
Hard Lefschetz Theorem for Nonrational Polytopes
Kalle Karu
The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomo…
Torification and Factorization of Birational Maps
Dan Abramovich, Kalle Karu, Kenji Matsuki +1
Building on the work of the fourth author in math.AG/9904074, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between comple…