Related papers: A Vanishing Result for Toric Varieties Associated …

Call a normal complex projective variety $X$ Koll\'ar-hyperbolic if any nonconstant map from a smooth projective curve to $X$ induces a nontrivial homomorphism of \'etale fundamental groups. Examples include (a) smooth varieties with finite…

We provide a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace K inside the second exterior product of a vector space, as well as a sharp upper bound for its Hilbert function.…

A tropical expansion is a degeneration of a toroidal embedding, induced by a polyhedral subdivision of its tropicalisation. Each irreducible component of a tropical expansion admits a collapsing map down to a stratum of the original…

A toric variety is a normal complex variety which is completely described by combinatorial data, namely by a fan of strongly convex rational (with respect to a lattice) cones. Due to this rationality condition, toric varieties are…

This paper gives computations of all the $G$-theory groups of several classes of simplicial toric varieties, including all affine toric surfaces when the base field is algebraically closed and has characteristic zero, all weighted…

Let $G=PSO(2n+1, \mathbb{C}) (n \ge 3)$ and $B$ be the Borel subgroup of $G$ containing maximal torus $T$ of $G.$ Let $w$ be an element of Weyl group $W$ and $X(w)$ be the Schubert variety in the flag variety $G/B$ corresponding to $w.$ Let…

This work concerns the study of properties of a group of Koszul algebras coming from the toric ideals of a chordal bipartite infinite family of graphs (alternately, these rings may be interpreted as coming from determinants of certain…

Given a boundary divisor $B$ on a projective toric variety $X$ such that $(X, B)$ is klt, we establish the Kawamata-Viehweg vanishing theorem for $(X, B)$.

Given any toric subvariety $Y$ of a smooth toric variety $X$ of codimension $k$, we construct a length $k$ resolution of $\mathcal O_Y$ by line bundles on $X$. Furthermore, these line bundles can all be chosen to be direct summands of the…

Let G be a complex, connected, reductive algebraic group with Weyl group W and Steinberg variety Z. We show that the graded Borel-Moore homology of Z is isomorphic to the smash product of the coinvariant algebra of W and the group algebra…

We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete discretely valued field, its continuous K-groups vanish in degrees below the negative of the…

For a toric variety X_P determined by a rational polyhedral fan P in a lattice N, Payne shows that the equivariant Chow cohomology of X_P is the Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use the…

Let $k$ be a finite field, a $p$-adic field or a number field. Let $K$ be a finite extension of the Laurent series field in $m$ variables $k((x_1,...,x_m))$ or, more generally, a finite extension of the field of rational functions…

The toral rank conjecture speculates that the sum of the Betti numbers of a compact manifold admitting a free action of a torus of rank $r$ is bounded from below by $2^r$. Clearly, such an action yields a torus bundle, and, more generally,…

Let $G$ be a simple algebraic group of adjoint type over $\mathbb{C},$ whose root system is of type $F_{4}.$ Let $T$ be a maximal torus of $G$ and $B$ be a Borel subgroup of $G$ containing $T.$ Let $w$ be an element of Weyl group $W$ and…

CORRECTION. One of the main results in this paper contains a fatal error. We cannot conclude the existence of nontrivial vector bundles on X from the nontriviality of its K-group. The K-group that is computed here is the Grothendieck group…

This paper is concerned with the relationships between two concepts, vanishing of cohomology groups and the structure of free resolutions. In particular, we study the connection between vanishing theorems for the local cohomology of…

A root system $\Phi$ of rank $n$ determines an $n$-dimensional smooth projective toric variety $X(\Phi)$ associated with the fan of its Weyl chambers. For the root system of type $A_n$, this variety is the well-known permutohedral variety…

The purpose of this paper is to prove Ein--Lazarsfeld's conjecture on asymptotic vanishing of syzygies of algebraic varieties. This result, together with Ein--Lazarsfeld's asymptotic nonvanishing theorem, describes the overall picture of…

We consider a complete nonsingular variety $X$ over $\bC$, having a normal crossing divisor $D$ such that the associated logarithmic tangent bundle is generated by its global sections. We show that $H^i\big(X, L^{-1} \otimes \Omega_X^j(\log…