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Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians
We study the space of non-simple polarised abelian surfaces. Specifically, we describe for which pairs ( m , n ) the locus of polarised abelian surfaces...
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Diffeomorphic Registration of 3D Surfaces with Point and Curve Landmarks
This paper proposes a novel method to compute the diffeomorphic registration of 3D surfaces with point and curve feature landmarks. First the...
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Approximating Maximum Integral Multiflows on Bounded Genus Graphs
We devise the first constant-factor approximation algorithm for finding an integral multi-commodity flow of maximum total value for instances where...
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The étale fundamental group of moduli of parahoric group scheme torsors over a curve
Let X be a smooth projective curve over an algebraically closed field k . Let G be an almost simple simply-connected group over k . Let
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A Symplectic Dynamics Proof of the Degree–Genus Formula
We classify global surfaces of section for the Reeb flow of the standard contact form on the 3-sphere (defining the Hopf fibration), with boundaries...
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Introduction to Plane Tropical Curve Counts
This lecture is aimed at newcomers to tropical geometry.
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On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit 3-Ball
We prove that the area of each nonflat genus zero free boundary minimal surface embedded in the unit 3-ball is less than the area of its radial...
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Lagrangian skeleta and plane curve singularities
We construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities.
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Quantum ergodicity for Eisenstein series on hyperbolic surfaces of large genus
We give a quantitative estimate for the quantum mean absolute deviation on hyperbolic surfaces of finite area in terms of geometric parameters such...
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Surfaces of Genus g = 0
Theorem 7.1 (Uniformization Theorem for g = 0). Let (S,J) be a J-surface of genus 0.
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Curve shortening flow on Riemann surfaces with conical singularities
We study the curve shortening flow on Riemann surfaces with finitely many conformal conical singularities. If the initial curve is passing through...
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Birational geometry of Beauville–Mukai systems I: the rank three and genus two case
We study wall-crossing for the Beauville–Mukai system of rank three on a general genus two K3 surface. We show that such a system is related to the...
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Quantum Curve and Bilinear Fermionic Form for the Orbifold Gromov–Witten Theory of ℙ[r]
We construct the quantum curve for the Baker–Akhiezer function of the orbifold Gromov–Witten theory of the weighted projective line ℙ[ r ]....
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Global surfaces of section with positive genus for dynamically convex Reeb flows
We establish some new existence results for global surfaces of section of dynamically convex Reeb flows on the three-sphere. These sections often...