Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2019, Volume 371, Issue 2, pp. 1119 - 1149

We give an explicit description of fundamental domains associated with the p-adic uniformisation of families of Shimura curves of discriminant Dp and level N...

Shimura curves | Mumford curves | p-adic fundamental domains | MATHEMATICS | UNIFORMIZATION | CONSTRUCTION | POINTS

Shimura curves | Mumford curves | p-adic fundamental domains | MATHEMATICS | UNIFORMIZATION | CONSTRUCTION | POINTS

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 05/2015, Volume 68, Issue 2, pp. 259 - 284

Mumford showed that Schottky subgroups of PGL(2,K) give rise to certain curves, now called Mumford curves, over a non-archimedean field K...

Tropical geometry | Mumford curve | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | ANALYTIC CONSTRUCTION | Algorithms

Tropical geometry | Mumford curve | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | ANALYTIC CONSTRUCTION | Algorithms

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2016, Volume 165, Issue 16, pp. 3189 - 3240

Let X be a curve of genus g >= 2 over a number field F of degree d = [F : Q]. The conjectural existence of a uniform bound N(g, d) on the number #X(F...

MATHEMATICS | REDUCTION | CHABAUTY | GEOMETRY

MATHEMATICS | REDUCTION | CHABAUTY | GEOMETRY

Journal Article

Compositio mathematica, ISSN 0010-437X, 11/2015, Volume 151, Issue 11, pp. 2076 - 2130

We prove by the Hilbert–Mumford criterion that a slope stable polarized weighted pointed nodal curve is Chow asymptotic stable...

Chow stability | geometric invariant theory | one parameter subgroups | K-stability | Chow weight | asymptotic stability | Hilbert-Mumford criterion | Donaldson-Futaki invariant | moduli of curves | BUNDLES | VARIETIES | MODULI | MATHEMATICS | GIT STABILITY | COMPACTIFICATION | Studies | Theoretical mathematics | Slopes | Sheaves | Stability | Criteria | Asymptotic properties

Chow stability | geometric invariant theory | one parameter subgroups | K-stability | Chow weight | asymptotic stability | Hilbert-Mumford criterion | Donaldson-Futaki invariant | moduli of curves | BUNDLES | VARIETIES | MODULI | MATHEMATICS | GIT STABILITY | COMPACTIFICATION | Studies | Theoretical mathematics | Slopes | Sheaves | Stability | Criteria | Asymptotic properties

Journal Article

1980, Lecture notes in mathematics, ISBN 0387102299, Volume 817., viii, 316

Book

IEEE Transactions on Image Processing, ISSN 1057-7149, 08/2001, Volume 10, Issue 8, pp. 1169 - 1186

...) paradigm from a curve evolution perspective. In particular, we let a set of deformable contours define the boundaries between regions in an image where we model...

Image segmentation | Interpolation | Computer vision | Smoothing methods | Image processing | Noise reduction | Stochastic processes | Application software | Image reconstruction | Active contours | Reconstruction | Curve evolution | Segmentation | Image magnification | Level sets methods | Boundary-value stochastic processes | Mumford-Shah functional | Missing data problems | Snakes | Image interpolation | Denoising | boundary-value stochastic processes | curve evolution | LEVEL SET APPROACH | VISION | image magnification | level sets methods | missing data problems | snakes | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | denoising | image interpolation | AREA | MOTION | reconstruction | segmentation | active contours | ACTIVE CONTOUR MODELS | FLOWS | ANISOTROPIC DIFFUSION | Research | Studies | Evolution | Algorithms | Smoothing | Contours | Images | Mathematical models

Image segmentation | Interpolation | Computer vision | Smoothing methods | Image processing | Noise reduction | Stochastic processes | Application software | Image reconstruction | Active contours | Reconstruction | Curve evolution | Segmentation | Image magnification | Level sets methods | Boundary-value stochastic processes | Mumford-Shah functional | Missing data problems | Snakes | Image interpolation | Denoising | boundary-value stochastic processes | curve evolution | LEVEL SET APPROACH | VISION | image magnification | level sets methods | missing data problems | snakes | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | denoising | image interpolation | AREA | MOTION | reconstruction | segmentation | active contours | ACTIVE CONTOUR MODELS | FLOWS | ANISOTROPIC DIFFUSION | Research | Studies | Evolution | Algorithms | Smoothing | Contours | Images | Mathematical models

Journal Article

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 3/2017, Volume 58, Issue 1, pp. 47 - 67

In the present paper, we investigate the question if the skeleton of a Mumford curve of genus two can be tropicalized faithfully in dimension three, i.e...

Geometry | Algebra | Berkovich spaces | Convex and Discrete Geometry | Tropicalization | Tropical geometry | Algebraic Geometry | 14H30 | Mathematics | Mumford curves | 14T05 | 14H45

Geometry | Algebra | Berkovich spaces | Convex and Discrete Geometry | Tropicalization | Tropical geometry | Algebraic Geometry | 14H30 | Mathematics | Mumford curves | 14T05 | 14H45

Journal Article

Kodai mathematical journal, ISSN 0386-5991, 2018, Volume 41, Issue 2, pp. 240 - 263

... of the projective line by Mumford curves over complete discrete valuation fields of positive characteristic p...

cyclic covering | Mumford curve | rigid analytic geometry | Rigid analytic geometry | Cyclic covering | MATHEMATICS

cyclic covering | Mumford curve | rigid analytic geometry | Rigid analytic geometry | Cyclic covering | MATHEMATICS

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2014, Volume 397, pp. 47 - 67

We will give a pure combinatorial proof of the Eisenbud–Goto conjecture for arbitrary monomial curves...

Eisenbud–Goto conjecture | Castelnuovo–Mumford regularity | Simplicial affine semigroup rings | Monomial curves | Eisenbud-Goto conjecture | Secondary | Castelnuovo-Mumford regularity | Primary | MATHEMATICS | CODIMENSION | COHEN-MACAULAY SCHEMES | REDUCTION NUMBER

Eisenbud–Goto conjecture | Castelnuovo–Mumford regularity | Simplicial affine semigroup rings | Monomial curves | Eisenbud-Goto conjecture | Secondary | Castelnuovo-Mumford regularity | Primary | MATHEMATICS | CODIMENSION | COHEN-MACAULAY SCHEMES | REDUCTION NUMBER

Journal Article

Journal of Algebra, ISSN 0021-8693, 12/2012, Volume 372, pp. 584 - 594

In this paper, we are interested in the generic initial ideals of singular projective curves with respect to the graded lexicographic order...

Castelnuovo–Mumford regularity | Partial elimination ideal | Graded lexicographic order | Generic initial ideal | Singular projective curve | THREEFOLDS | MATHEMATICS | Castelnuovo-Mumford regularity | CODIMENSION 2 | DEGREE-COMPLEXITY | SMOOTH SURFACES | Generic drugs

Castelnuovo–Mumford regularity | Partial elimination ideal | Graded lexicographic order | Generic initial ideal | Singular projective curve | THREEFOLDS | MATHEMATICS | Castelnuovo-Mumford regularity | CODIMENSION 2 | DEGREE-COMPLEXITY | SMOOTH SURFACES | Generic drugs

Journal Article

Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 06/2010, Volume 46, Issue 2, pp. 219 - 253

We construct a rigid analytical regulator for the K-2 of Mumford curves, a non-archimedean analogue of th9e complex analytical Beilinson-Bloch-Deligne regulator.

MATHEMATICS | regulator | Mumford curves

MATHEMATICS | regulator | Mumford curves

Journal Article

Bulletin of the American Mathematical Society, ISSN 0273-0979, 04/2020, Volume 57, Issue 2, pp. 171 - 267

...}^1, modulo the group of projective transformations of \mathbb{P}^1; and then the moduli space of curves...

improper action | Deligne-Mumford compactification | weakly proper action | W-curves | MODULI SPACES | stabilizers of curves | tree-of-spheres | moduli space of divisors | RATIONALITY | proper action | MATHEMATICS | weak orbifolds | smooth complex curves | Moduli space of curves | REAL | effective 1-cycles | orbifolds | algebraic set | rational homology manifold | group actions

improper action | Deligne-Mumford compactification | weakly proper action | W-curves | MODULI SPACES | stabilizers of curves | tree-of-spheres | moduli space of divisors | RATIONALITY | proper action | MATHEMATICS | weak orbifolds | smooth complex curves | Moduli space of curves | REAL | effective 1-cycles | orbifolds | algebraic set | rational homology manifold | group actions

Journal Article

Annals of mathematics, ISSN 0003-486X, 5/2020, Volume 191, Issue 3, pp. 949 - 1001

...). We apply this strategy to prove a conjecture of Bogomolov, Fu, and Tschinkel asserting uniform bounds on the number of common torsion points of elliptic curves in the case of two Legendre curves over ℂ...

torsion points | MATHEMATICS | arithmetic intersection | EQUIDISTRIBUTION | Manin-Mumford | Lattes maps | VARIETIES | preperiodic points | CANONICAL HEIGHTS | elliptic curves | non-archimedean potential theory

torsion points | MATHEMATICS | arithmetic intersection | EQUIDISTRIBUTION | Manin-Mumford | Lattes maps | VARIETIES | preperiodic points | CANONICAL HEIGHTS | elliptic curves | non-archimedean potential theory

Journal Article

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, ISSN 0025-5858, 4/2013, Volume 83, Issue 1, pp. 83 - 99

We relate two different partial p-adic analogues of the classical Riemann-Hilbert correspondence on curves...

Berkovich analytic space | 14H30 | Mathematics | Topology | 11G20 | 14G22 | Geometry | Algebra | 14H60 | 14H70 | p -adic geometry | Parallel transport | Number Theory | Differential Geometry | Combinatorics | Riemann-Hilbert-correspondence | p-adic geometry | MUMFORD CURVES | MATHEMATICS | SPACES | RIGID GEOMETRY | VECTOR-BUNDLES | Heterocyclic compounds

Berkovich analytic space | 14H30 | Mathematics | Topology | 11G20 | 14G22 | Geometry | Algebra | 14H60 | 14H70 | p -adic geometry | Parallel transport | Number Theory | Differential Geometry | Combinatorics | Riemann-Hilbert-correspondence | p-adic geometry | MUMFORD CURVES | MATHEMATICS | SPACES | RIGID GEOMETRY | VECTOR-BUNDLES | Heterocyclic compounds

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2019, Volume 517, pp. 119 - 166

... is a curve of genus 0. As abstract group Γ is an amalgam of a finite tree of finite groups...

Rigid geometry | Mumford groups | Discontinuous groups | Stratified bundles | Mumford curves | Amalgams | Orbifolds | MAXIMAL AUTOMORPHISM GROUP | SUBGROUPS | PGL(K) | To be checked by Faculty | MATHEMATICS

Rigid geometry | Mumford groups | Discontinuous groups | Stratified bundles | Mumford curves | Amalgams | Orbifolds | MAXIMAL AUTOMORPHISM GROUP | SUBGROUPS | PGL(K) | To be checked by Faculty | MATHEMATICS

Journal Article

Communications in algebra, ISSN 0092-7872, 09/2020, Volume 48, Issue 9, pp. 3724 - 3742

In this paper we explicitly describe the symbolic powers of the ideal defining the curve in parametrized by where q, m are positive integers, and We show that the symbolic blowup algebra is Noetherian and Gorenstein...

1305 | symbolic Rees algebra | resurgence | Waldschmidt constant | Primary: 13A30 | Castelnuovo-Mumford regularity | MATHEMATICS | RESURGENCES | POWERS | IDEALS | ASYMPTOTIC-BEHAVIOR

1305 | symbolic Rees algebra | resurgence | Waldschmidt constant | Primary: 13A30 | Castelnuovo-Mumford regularity | MATHEMATICS | RESURGENCES | POWERS | IDEALS | ASYMPTOTIC-BEHAVIOR

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2006, Volume 358, Issue 1, pp. 267 - 284

In this paper we prove that the regularity of a connected curve is bounded by its degree minus its codimension plus 1...

Conic sections | Algebra | Mathematical theorems | Hyperplanes | Secant function | Secant lines | Curves | Connected curves | Castelnuovo-Mumford regularity | Eisenbud-Goto conjecture | THREEFOLDS | MATHEMATICS | GENERIC PROJECTIONS | SMOOTH SURFACES | connected curves

Conic sections | Algebra | Mathematical theorems | Hyperplanes | Secant function | Secant lines | Curves | Connected curves | Castelnuovo-Mumford regularity | Eisenbud-Goto conjecture | THREEFOLDS | MATHEMATICS | GENERIC PROJECTIONS | SMOOTH SURFACES | connected curves

Journal Article

Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2010, Volume 46, Issue 2, pp. 219 - 253

Journal Article

IEEE Transactions on Image Processing, ISSN 1057-7149, 09/2017, Volume 26, Issue 9, pp. 4414 - 4429

Variational models are known to work well for addressing image restoration/regularization problems. However, most of the methods proposed in the literature are...

variational methods | Image edge detection | Piecewise linear approximation | Mumford-Shah | Blake-Zisserman | block-coordinate descent method | Minimization | Approximation algorithms | Multiband image | Numerical models | Image restoration | Mathematical model | piecewise linear approximation | RESTORATION | GRADIENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | EDGE-DETECTION | COLOR | SEGMENTATION | MULTIVALUED IMAGES | JUMPS | Usage | Mathematical models | Computer-generated environments | Research | Computer simulation

variational methods | Image edge detection | Piecewise linear approximation | Mumford-Shah | Blake-Zisserman | block-coordinate descent method | Minimization | Approximation algorithms | Multiband image | Numerical models | Image restoration | Mathematical model | piecewise linear approximation | RESTORATION | GRADIENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | EDGE-DETECTION | COLOR | SEGMENTATION | MULTIVALUED IMAGES | JUMPS | Usage | Mathematical models | Computer-generated environments | Research | Computer simulation

Journal Article

20.
Full Text
Poincaré duality for the tropical Dolbeault cohomology of non-archimedean Mumford curves

Journal of Number Theory, ISSN 0022-314X, 06/2018, Volume 187, pp. 344 - 371

We calculate the tropical Dolbeault cohomology for the analytifications of P1 and Mumford curves over non-archimedean fields...

Non-archimedean curves | Poincaré duality | Berkovich spaces | Smooth differential forms on Berkovich spaces | Mumford curves | Non-archimedean geometry | Tropicalizations | MATHEMATICS | Poincare duality | Smooth differential forms on

Non-archimedean curves | Poincaré duality | Berkovich spaces | Smooth differential forms on Berkovich spaces | Mumford curves | Non-archimedean geometry | Tropicalizations | MATHEMATICS | Poincare duality | Smooth differential forms on

Journal Article

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