Related papers: Intersection complexes of fans and toric varieties
The title theorem is proved by example: an algebra of binary relations, closed under intersection and composition, that is not isomorphic to any such algebra on a finite set.
We provide an overview of the combinatorial theory of horospherical varieties using coloured fans, a generalization of the combinatorial theory of toric varieties using polyhedral fans.
In this corrigendum to arXiv:2305.02973, we justify that the motivation behind Conjecture 5.1 is based on a mistaken notion. Moreover, we prove a stronger theorem that disproves the conjecture, and obtain an optimal gradient vector field on…
The paper has been withdrawn due to a crucial error in section 3.
We show that the components, appearing in the decomposition theorem for contraction maps of torus actions of complexity one, are intersection cohomology complexes of even codimensional subvarieties. As a consequence, we obtain the vanishing…
We introduce the notion of a multi-fan. It is a generalization of that of a fan in the theory of toric variety in algebraic geometry. Roughly speaking a toric variety is an algebraic variety with an action of algebraic torus of the same…
The SYZ conjecture suggests a folklore that "Lagrangian multi-sections are mirror to holomorphic vector bundles". In this paper, we prove this folklore for Lagrangian multi-sections inside the cotangent bundle of a vector space, which are…
We show that a conjecture of Einsiedler, Kapranov, and Lind on adelic amoebas of subvarieties of tori and their intersections with open halfspaces of complementary dimension is false for subvarieties of codimension greater than one that…
The proof of Theorem 5.12 in [C.M. Drupieski, On injective modules and support varieties for the small quantum group, Int. Math. Res. Not. 2011 (2011), 2263-2294] does not make sense as written because the algebra…
We will announce two theorems. The first theorem will classify all topological types of degenerate fibers appearing in one-parameter families of Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The second theorem…
Withdrawn by the authors, the main theorem is incorrect
This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.
We continue our study of the Noether-Lefschetz loci in toric varieties and investigate deformation of pairs (V,X) where V is a complete intersection subvariety and X a quasi-smooth hypersurface in a odd dimensional simplicial projective…
We provide some new local obstructions to approximating tropical curves in smooth tropical surfaces. These obstructions are based on the relation between tropical and complex intersection theories which is also established here. We give two…
A Cremona transformation of five-dimensional projective space is constructed. The degree of the transformation is 7. The inequalities of Fano are not fulfilled for this transformation.
Reason for withdrawal: There is a serious mistake in the calculation of the divisor of the rational section used in the proof of Prop. 2.2.1., and with the correct value the argument does not work.
Associated to a toric variety $X$ of dimension $r$ over a field $k$ is a fan $\Delta$ on $\Bbb R^r$. The fan $\Delta$ is a finite set of cones which are in one-to-one correspondence with the orbits of the torus action on $X$. The fan…
Faber, Muller and Smith used complete sums of conic modules to construct non-commutative crepant resolutions (NCCR) of simplicial toric algebras. We link these conic modules to the Bondal-Thomsen collection of line bundles on smooth toric…
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 Betti numbers h_i of X and the numbers g_i = h_i-h_{i-1}. If…
This paper has been subsumed by math.AG/0502240