arXiv research

Researchers prove K-semistability for cscK manifolds with transcendental cohomology.

Transcendental holomorphic Morse inequalities aim at characterizing the positivity of transcendental cohomology classes of type $(1,1)$. In this paper, we prove a weak version of Demailly's conjecture on transcendental Morse inequalities on compact Kähler manifolds. And as a consequence, we partially improve a result o…

Researchers prove an algebraic structure for transcendental Hodge lattices and apply it to symplectic embeddings.

Introduces non-Archimedean metrics for pseudoeffective classes on Kähler manifolds.

The purpose of this paper is to establish an injectivity theorem generalized to pseudo-effective line bundles with transcendental (non-algebraic) singular hermitian metrics and multiplier ideal sheaves. As an application, we obtain a Nadel type vanishing theorem. For the proof, we study the asymptotic behavior of the h…

Unconditional proof of Demailly's transcendental Morse inequality for higher cohomology classes using a general gauge-fixing for the Monge-Ampère-type equation.

Study convexity of Mabuchi functional in big cohomology classes.

Analyzes log canonical pairs using harmonic integrals and dbar-equation theory.

Study shows small transcendental simplicial volumes exist on manifolds.

Associated with a smooth, $d$-closed $(1, 1)$-form $α$ of possibly non-rational De Rham cohomology class on a compact complex manifold $X$ is a sequence of asymptotically holomorphic complex line bundles $L_k$ on $X$ equipped with $(0, 1)$-connections $\bar\partial_k$ for which $\bar\partial_k^2\neq 0$. Their study was…

The paper extends intersection theory for b-divisors, proving monotonicity and volume inequalities.

Proves existence of Kähler-Einstein metrics in big cohomology classes.

Defines operations in non-Archimedean metrics theory.

New invariant of virtual knots generalizes existing polynomial invariants.

Study of holomorphic correspondences combining entire maps and Fuchsian groups.

Weak base-point freeness leads to Kähler-Ricci flow diameter bounds.

TAMD prevents degeneracy in finite mixtures, offering strong guarantees but modest practical improvements.

Paper introduces a new invariant for planar knotoids.

Yair Minsky showed that punctured torus groups are classified by a pair of ending laminations (ν_-,ν_+). In this note, we show that there are ending laminations ν_+ such that for any choice of ν_-, the punctured torus group is transcendental as a subgroup of PSL_2 C.

Study shows volumes of complex classes can be represented by convex bodies.

Study b-divisors on Kähler manifolds linking them to currents.

Algorithm constructs integrals of hyperexponential 1-forms.

We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a numb…

Study on the number of volume-preserving Dehn fillings of hyperbolic 3-manifolds.

Study TQFT representations for surfaces with boundary, showing irreducibility at prime roots of unity and Zariski density for transcendental parameters.

Projective varieties remain stable under close polarizations, extending to Kähler cones.

Paper constructs connections on curves with specific Galois groups.

Proves algebraicity of maps to hyperbolic varieties using specialization techniques.

This research extends quasiplurisubharmonic functions on compact Kähler manifolds.

We prove the qualitative part of Demailly's conjecture on transcendental Morse inequalities for differences of two nef classes satisfying a numerical relative positivity condition on an arbitrary compact Kähler (and even more general) manifold. The result improves on an earlier one by J. Xiao whose constant $4n$ featur…

Analytic curves linked to algebraic ones via Schottky groups.

We show that the distance trisector curve is not an algebraic curve, as was conjectured in the founding paper by T. Asano, J. Matousek and T. Tokoyama: "The distance trisector curve", Advances in Math., 212, 338-360 (2007).

In this short paper, we will give a simple and transcendental proof for Mok's theorem of the generalized Frankel conjecture. This work is based on the maximum principle in \cite{BS2} proposed by Brendle and Schoen.

In this paper we give examples of closed smooth submanifolds of RP^n which are isotopic to nonsingular projective subvarieties of RP^n but they can not be isotopic to the real parts of nonsingular complex projective subvarieties of CP^n.

Paper connects Stokes phenomena to quantum groups and Poisson-Lie groups.

The study connects free subgroups in a specific group to hypermaps, deriving generating series and asymptotic formulas.

Algorithm constructs algebraic curves from translation surfaces.

The paper classifies periodic solitons in curve flows on the light-cone.

Paper studies K-polystability of cscK manifolds with holomorphic vector fields.

Let $\{α\}$ and $\{β\}$ be nef cohomology classes of bidegree $(1,\,1)$ on a compact $n$-dimensional Kähler manifold $X$ such that the difference of intersection numbers $\{α\}^n - n\,\{α\}^{n-1}.\,\{β\}$ is positive. We solve in a number of special but rather inclusive cases the quantitative part of Demailly's Transce…

We give examples of finitely presented groups containing elements with irrational (in fact, transcendental) stable commutator length, thus answering in the negative a question of M. Gromov. Our examples come from 1-dimensional dynamics, and are related to the generalized Thompson groups studied by M. Stein, I. Liousse …

The paper explores knot invariants using quantum dilogarithm representations and compares them to compact cases.

The paper studies extremal hypersurfaces in ellipsoids using centro-affine geometry.

Let X be a compact complex manifold equipped with a smooth (but not necessarily positive) closed form theta of one-one type. By a well-known envelope construction this data determines a canonical theta-psh function u which is not two times differentiable, in general. We introduce a family of regularizations of u, param…

This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal treatement of Teichmuller space and higher genus moduli spaces. The point of view is ge…

Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation. In the limit of continuous trad…

The paper proves a unique cscK metric for uniformly K-stable Kähler manifolds.

An old problem asks whether a Riemannian manifold can be isospectral to a Riemannian orbifold with nontrivial singular set. In this short note we show that under the assumption of Schanuel's conjecture in transcendental number theory, this is impossible whenever the orbifold and manifold in question are length-commensu…