Zobrazeno 1 - 10
of 172
pro vyhledávání: '"Shaw, Kristin"'
We describe a canonical compactification of a polyhedral complex in Euclidean space. When the recession cones of the polyhedral complex form a fan, the compactified polyhedral complex is a subspace of a tropical toric variety. In this case, the proce
Externí odkaz:
http://arxiv.org/abs/2012.12161
The family of complex projective surfaces in projective three space of degree $d$ having precisely $\delta$ nodes as their only singularities has codimension $\delta$ in the linear system of surfaces of degree $d$ for sufficiently large $d$ and is of
Externí odkaz:
http://arxiv.org/abs/1910.08585
We establish variants of the Lefschetz hyperplane section theorem for the integral tropical homology groups of tropical hypersurfaces of toric varieties. It follows from these theorems that the integral tropical homology groups of non-singular tropic
Externí odkaz:
http://arxiv.org/abs/1907.06420
Autor:
Mohammadi, Fatemeh, Shaw, Kristin
Publikováno v:
Algebraic Combinatorics, Volume 2 (2019) no. 6, p. 1109-1124
We study the algebraic combinatorics of monomial degenerations of Pl\"ucker forms which is governed by matching fields in the sense of Sturmfels and Zelevinsky. We provide a necessary condition for a matching field to yield a Khovanskii basis of the
Externí odkaz:
http://arxiv.org/abs/1809.01026
Autor:
Renaudineau, Arthur, Shaw, Kristin
We prove a bound conjectured by Itenberg on the Betti numbers of real algebraic hypersurfaces near non-singular tropical limits. These bounds are given in terms of the Hodge numbers of the complexification. To prove the conjecture we introduce a real
Externí odkaz:
http://arxiv.org/abs/1805.02030
Publikováno v:
Ãpijournal de Géométrie Algébrique, Volume 2 (November 19, 2018) epiga:4126
For a tropical manifold of dimension n we show that the tropical homology classes of degree (n-1, n-1) which arise as fundamental classes of tropical cycles are precisely those in the kernel of the eigenwave map. To prove this we establish a tropical
Externí odkaz:
http://arxiv.org/abs/1711.07900
Autor:
Kummer, Mario, Shaw, Kristin
We introduce the separating semigroup of a real algebraic curve of dividing type. The elements of this semigroup record the possible degrees of the covering maps obtained by restricting separating morphisms to the real part of the curve. We also intr
Externí odkaz:
http://arxiv.org/abs/1707.08227
We define Chern-Schwartz-MacPherson (CSM) cycles of an arbitrary matroid. These are balanced weighted fans supported on the skeleta of the corresponding Bergman fan. In the case that the matroid arises from a complex hyperplane arrangement A, we show
Externí odkaz:
http://arxiv.org/abs/1707.07303
This chapter provides a guide to our polymake extension cellularSheaves. We first define cellular sheaves on polyhedral complexes in Euclidean space, as well as cosheaves, and their (co)homologies. As motivation, we summarise some results from toric
Externí odkaz:
http://arxiv.org/abs/1612.09526
We establish a canonical isomorphism between two bigraded cohomology theories for polyhedral spaces: Dolbeault cohomology of superforms and tropical cohomology. Furthermore, we prove Poincar\'e duality for cohomology of tropical manifolds, which are
Externí odkaz:
http://arxiv.org/abs/1512.07409