Related papers: Newton-Okounkov bodies and complexity functions

Given a smooth Mori dream space $X$ we construct a model dominating all the small $\mathbb{Q}$-factorial modifications via tropicalization. This construction allows us to recover a Minkowski basis for the Newton-Okounkov bodies of divisors…

Examples by Poletsky and the author and by Zwonek show the existence nowhere extendable holomorphic functions with the property that the pluripolar hull of their graphs is much larger than the graph of the respective functions and contains…

In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and…

In recent work, Lusztig's positive root vectors (with respect to a distinguished choice of reduced decomposition of the longest element of the Weyl group) were shown to give a quantum tangent space for every $A$-series Drinfeld--Jimbo full…

We find the precise number of non-K\"ahler $SO(2n)$-invariant Einstein metrics on the generalized flag manifold $M=SO(2n)/U(p)\times U(n-p)$ with $n\geq 4$ and $2\leq p\leq n-2$. We use an analysis on parametric systems of polynomial…

For fixed compact connected Lie groups H \subseteq G, we provide a polynomial time algorithm to compute the multiplicity of a given irreducible representation of H in the restriction of an irreducible representation of G. Our algorithm is…

Bott vanishing is a strong vanishing result for the cohomology of exterior powers of the cotangent bundle twisted by ample line bundles. Buch-Thomsen-Lauritzen-Mehta conjectured that partial flag varieties (which are not products of…

We investigate the multiplier rigidity problem for polynomial automorphisms of $\mathbf{C}^2$. A first result states that a complex H\'enon map of given degree is determined up to finitely many choices by its multiplier spectrum, or more…

Let $X$ be a smooth projective variety. We construct partial Okounkov bodies associated to Hermitian pseudo-effective line bundles $(L,\phi)$ on $X$. We show that partial Okounkov bodies are universal invariants of the singularity of…

We prove that under certain assumptions a supermanifold of flags is rigid, this is its complex structure does not admit any non-trivial small deformation. Moreover under the same assumptions we show that a supermanifold of flags is unique…

We define and study the global Okounkov moment cone of a projective spherical variety X, generalizing both the global Okounkov body and the moment body of X defined by Kaveh and Khovanskii. Under mild assumptions on X we show that the…

We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit…

In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost…

We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…

We define an analogue of the Fox derivatives for differential polynomial algebras and give a criterion for differential algebraic dependence of a finite system of elements. In particular, we prove that differential algebraic dependence of a…

We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.-F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of $\mathbb{C}$…

We relate the structure factor $S(\mathbf{k} \to \mathbf{0})$ in a system of jammed hard spheres of number density $\rho$ to its complexity per particle $\Sigma(\rho)$ by the formula $S(\mathbf{k} \to \mathbf{0})=-1/…

In a previous paper we defined the concept of an affinized projective variety and its associated Hilbert series. We computed the Hilbert series for varieties associated to quadratic monomial ideals. In this paper we show how to apply these…

We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional…

It is expected that a totally invariant divisor of a non-isomorphic endomorphism of the complex projective space is a union of hyperplanes. In this paper, we compute an upper bound for the degree of such a divisor. As a consequence, we…