Related papers: Singular string polytopes and functorial resolutio…
Let X be a normal projective Q-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in X via the total stringy Chern class of X. This…
We analyze deformations of two-dimensional conformal field theory (CFT) from the perspective of classical bosonic closed string field theory (SFT). The latter can be viewed as a version of Wilsonian renormalization group (RG) improved…
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of…
Beilinson's resolution of the diagonal for complex projective space was generalized by Bayer-Popescu-Sturmfels for any unimodular toric variety. Here, we give a resolution of the diagonal for any smooth toric variety (viewed as a toric…
We study the relation between topological string theory and singularity theory using the partition function of $A_{N-1}$ topological string defined by matrix integral of Kontsevich type. Genus expansion of the free energy is considered, and…
We prove a combinatorial version of Thom's Isotopy Lemma for projection maps applied to any complex or real toric variety. Our results are constructive and give rise to a method for associating the Whitney strata of the projection to the…
We give a uniform proof for the conjectured Gromov width of coadjoint orbits of all compact connected simple Lie groups, by analyzing simplices in Newton-Okounkov bodies.
We give a definition of Newton non degeneracy independent of the system of generators defining the variety. This definition extends the notion of Newton non degeneracy to varieties that are not necessarily complete intersection. As in the…
We study static cosmic string solutions in the context of Bekenstein-type models. We show that there is a class of models of this type for which the classical Nielsen-Olesen vortex is still a valid solution. However, in general static…
In this paper we express any intersection number $(L_1\cdot\ldots\cdot L_d)$ of ample line bundles on an irreducible projective variety as the mixed volume $V(\Delta_{Y_\bullet}(L_1),\dots,\Delta_{Y_\bullet}(L_d))$ of their Newton-Okounkov…
Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus $\mathbf{g}\geq 2$ and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to…
Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…
Let $\SF^a_\lambda$ be the degenerate symplectic flag variety. These are projective singular irreducible $\bG_a^M$ degenerations of the classical flag varieties for symplectic group $Sp_{2n}$. We give an explicit construction for the…
We show (Theorem 3) that the symplectic reduction of the spatial $n$-body problem at non-zero angular momentum is a singular symplectic space consisting of two symplectic strata, one for spatial motions and the other for planar motions.…
We first prove some basic properties of Okounkov bodies, and give a characterization of Nakayama and positive volume subvarieties of a pseudoeffective divisor in terms of Okounkov bodies. Next, we show that each valuative and limiting…
In this note we focus on three independent problems on Okounkov bodies for projective varieties. The main goal is to present a geometric version of the classical Fujita Approximation Theorem, a Jow-type theorem and a cardinality formulae…
We prove an effective stabilization result for the sheaf cohomology groups of line bundles on flag varieties parametrizing complete flags in k^n, as well as for the sheaf cohomology groups of polynomial functors applied to the cotangent…
The purpose of this paper is to charazterize asymptotic base loci of line bundles on projective varieties via Newton-Okounkov bodies.
We consider the problem of finding sum of squares (sos) expressions to establish the non-negativity of a symmetric polynomial over a discrete hypercube whose coordinates are indexed by the $k$-element subsets of $[n]$. For simplicity, we…
Our first result realizes the toric variety of every marked chain-order polytope (MCOP) of the Gelfand--Tsetlin poset as an explicit Gr\"obner (sagbi) degeneration of the flag variety. This generalizes the…