Related papers: Toric weak Fano varieties associated to building s…
We give a precise relation between the mirror transformation and the Seidel elements for weak Fano toric Deligne-Mumford stacks. Our result generalizes the corresponding result for toric varieties proved by Gonz\'alez and Iritani in…
We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong…
The main result of this paper shows that a weak form of Tower Sealing holds in a generic extension of hod mice with a strong cardinal and a proper class of Woodin cardinals. We show Tower Sealing fails in such extensions in general. We show…
This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…
In this paper, we provide examples of Sarkisov links of type II between complex projective Fano threefolds $X$ with $\rho(X) = 1$. To show examples of these links, we study smooth weak Fano threefolds with extremal rays of type $E$. We…
We prove the generalised Mukai conjecture for $\mathbb{Q}$-factorial spherical Fano varieties. In this case, a stronger inequality holds featuring an extra term - the minimum absolute complexity of a log Calabi-Yau pair - which measures how…
We prove a weak version of a bigness criterion for equivariant vector bundles on toric varieties.
We completely classify the Q-factorial terminal toric Fano three-folds such that the sum of the squared torus invariant prime divisors is non-negative.
We show that the classifying category C(T) of a dependent type theory T with axioms for identity types admits a non-trivial weak factorisation system. We provide an explicit characterisation of the elements of both the left class and the…
We show that any $(\C ^*)^n$-invariant stably complex structure on a topological toric manifold of dimension $2n$ is integrable. We also show that such a manifold is weakly $(\C ^*)^n$-equivariantly isomorphic to a toric manifold.
We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1) The structure of the Gauss map of a toric variety is…
As a special case of a conjecture by Schwede and Smith, we prove that a smooth complex projective threefold with nef anti-canonical divisor is weak Fano if it is of globally $F$-regular type.
Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…
We show that the isolated invariant branches globalize to algebraic curves, when we consider weak toric type complex hyperbolic foliations on projective toric ambient surfaces. To do it, we pass through a characterization of weak toric type…
We study the equivariant real structures on complex horospherical varieties, generalizing classical results known for toric varieties and flag varieties. In particular, we obtain a necessary and sufficient condition for the existence of…
In this note we collect some results on the deformation theory of toric Fano varieties.
Some diophantine aspects of projective toric varieties: We present several faces of projective toric varieties, of interest from the point of view of diophantine geometry. We make explicit the theory on a number of meaningful examples and…
We classify rank two vector bundles on a Fano threefold of Picard rank one whose projectivizations are weak Fano. We also prove the existence of examples for each case of the classification result. Our classification includes detailed…
We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for…
We construct the algebra of fractions of a Weak Bialgebra relative to a suitable denominator set of group-like elements that is `almost central', a condition we introduce in the present article which is sufficient in order to guarantee…