Impact Factor: 0.5

Published since March 1, 2001

Advances in Geometry

ISSN: 1615-7168

Managing Editors: Theo Grundhöfer, Michael Joswig

Editorial Board: John Bamberg, Eiichi Bannai, Renzo Cavalieri, Izzet Coskun, Patrick Eberlein, Graziano Gentili, Martin Henk, William M. Kantor, Gabor Korchmaros, Alexander Kreuzer, Jeffrey C. Lagarias, Thomas Leistner, Rainer Löwen, Kaoru Ono, Daniel Plaumann, Francisco Santos, Steven H. Weintraub, Richard Weiss

About this journal

Objective
Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.

Topics

Finite geometry
Incidence geometry
Tits buildings
Combinatorial aspects of geometry and geometric combinatorics
Geometric group theory
Geometric aspects of Lie groups and of algebraic groups
Algebraic geometry
Topological geometry
Differential geometry
Convex sets and polytopes
Discrete geometry

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Research articles

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Leading journal in the field of geometry
Rigorous and thorough peer-review
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History

The journal was founded in 2001.

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Volume 23 Issue 3

August 2023

Publicly Available August 11, 2023

Frontmatter

Page range: i-iii

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August 11, 2023

Topology of tropical moduli spaces of weighted stable curves in higher genus

Siddarth Kannan, Shiyue Li, Stefano Serpente, Claudia He Yun

Page range: 305-314

Abstract

We study the topology of moduli spaces of weighted stable tropical curves Δ g , w with fixed genus and unit volume. The space Δ g , w arises as the dual complex of the divisor of singular curves in Hassett’s moduli space M g , w of weighted stable curves. When the genus is positive, we show that Δ g , w is simply connected for any choice of weight vector w . We also give a formula for the Euler characteristic of Δ g , w in terms of the combinatorics of the weight vector.

Open Access July 14, 2023

Explicit p-harmonic functions on the real Grassmannians

Elsa Ghandour, Sigmundur Gudmundsson

Page range: 315-321

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Abstract

We use the method of eigenfamilies to construct explicit complex-valued proper p -harmonic functions on the compact real Grassmannians. We also find proper p -harmonic functions on the real flag manifolds which do not descend onto any of the real Grassmannians.

August 9, 2023

Cohomogeneity one central Kähler metrics in dimension four

Thalia Jeffres, Gideon Maschler, Robert Ream

Page range: 323-344

Abstract

A Kähler metric is called central if the determinant of its Ricci endomorphism is constant; see [12]. For the case in which this constant is zero, we study on 4-manifolds the existence of complete metrics of this type which have cohomogeneity one for three unimodular 3-dimensional Lie groups: SU(2), the group E (2) of Euclidean plane motions, and a quotient by a discrete subgroup of the Heisenberg group nil 3 . We obtain a complete classification for SU(2), and some existence results for the other two groups, in terms of specific solutions of an associated ODE system.

August 11, 2023

Tropical Poincaré duality spaces

Edvard Aksnes

Page range: 345-370

Abstract

The tropical fundamental class of a rational balanced polyhedral fan induces cap products between tropical cohomology and tropical Borel–Moore homology. When all these cap products are isomorphisms, the fan is said to be a tropical Poincaré duality space . If all the stars of faces also are such spaces, such as for fans of matroids, the fan is called a local tropical Poincaré duality space . In this article, we first give some necessary conditions for fans to be tropical Poincaré duality spaces and a classification in dimension one. Next, we prove that tropical Poincaré duality for the stars of all faces of dimension greater than zero and a vanishing condition implies tropical Poincaré duality of the fan. This leads to necessary and sufficient conditions for a fan to be a local tropical Poincaré duality space. Finally, we use such fans to show that certain abstract balanced polyhedral spaces satisfy tropical Poincaré duality.

July 13, 2023

Isometries of wall-connected twin buildings

Sebastian Bischof, Bernhard Mühlherr

Page range: 371-388

Abstract

We introduce the notion of a wall-connected twin building and show that the local-to-global principle holds for these twin buildings. As each twin building satisfying Condition (co) (introduced in [7]) is wall-connected, we obtain a strengthening of the main result of [7] that covers also the thick irreducible affine twin buildings of rank at least 3.

July 13, 2023

On automorphisms of semistable G-bundles with decorations

Andres Fernandez Herrero

Page range: 389-400

Abstract

We prove a rigidity result for automorphisms of points of certain stacks admitting adequate moduli spaces. It encompasses as special cases variations of the moduli of G -bundles on a smooth projective curve for a reductive algebraic group G . For example, our result applies to the stack of semistable G -bundles, to stacks of semistable Hitchin pairs, and to stacks of semistable parabolic G -bundles. Similar arguments apply to Gieseker semistable G -bundles in higher dimensions. We present two applications of the main result. First, we show that in characteristic 0 every stack of semistable decorated G -bundles admitting a quasiprojective good moduli space can be written naturally as a G -linearized global quotient Y / G , so the moduli problem can be interpreted as a GIT problem. Secondly, we give a proof that the stack of semistable meromorphic G -Higgs bundles on a family of curves is smooth over any base in characteristic 0.

July 13, 2023

Abelian branched covers of rational surfaces

Robert Harris, Amey Joshi, B. Doug Park, Mainak Poddar

Page range: 401-411

Abstract

We study abelian covers of rational surfaces branched over line arrangements. We use these covers to address the geography problem for closed simply connected nonspin irreducible symplectic 4-manifolds with positive signature.

August 11, 2023

Polyhedral compactifications, I

Corina Ciobotaru, Linus Kramer, Petra Schwer

Page range: 413-436

Abstract

In this work we describe horofunction compactifications of metric spaces and finite-dimensional real vector spaces through asymmetric metrics and asymmetric polyhedral norms by means of nonstandard methods, that is, by ultrapowers of the spaces at hand. The polyhedral compactifications of the vector spaces carry the structure of stratified spaces with the strata indexed by dual faces of the polyhedral unit ball. Explicit neighborhood bases and descriptions of the horofunctions are provided.

Volume 23 (2023)

Volume 22 (2022)

Volume 21 (2021)

Volume 20 (2020)

Volume 19 (2019)

Volume 18 (2018)

Volume 17 (2017)

Volume 16 (2016)

Volume 15 (2015)

Volume 14 (2014)

Volume 13 (2013)

Volume 12 (2012)

Volume 11 (2011)

Volume 10 (2010)

Volume 9 (2009)

Volume 8 (2008)

Volume 7 (2007)

Volume 6 (2006)

Volume 5 (2005)

Volume 4 (2004)

Volume 3 (2003)

Volume 2 (2002)

Volume 1 (2001)

Journal Impact Factor	0.5	2022, Journal Citation Reports (Clarivate, 2023)
5-year Journal Impact Factor	0.5	2022, Journal Citation Reports (Clarivate, 2023)
Journal Citation Indicator	0.52	2022, Journal Citation Reports (Clarivate, 2023)
CiteScore	1.0	2022, Scopus (Elsevier B.V., 2023)
SCImago Journal Rank	0.393	2022, SJR (Scimago Lab, 2023; Data Source: Scopus)
Source Normalized Impact per Paper	0.839	2022, CWTS Journal Indicators (CWTS B.V., 2023; Data Source: Scopus)
Mathematical Citation Quotient	0.61

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Manuscript submission is done electronically by emailing a single PDF file (do not send any source files at this stage) to advgeom@mathematik.uni-wuerzburg.de.

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In this journal, authors have the option to publish their article under an open access license. Open Access allows you as an author to retain copyright and share your findings with colleagues and interested parties worldwide without any restraints.
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Editorial

Managing Editors

Theo Grundhöfer
Institut für Mathematik
Universität Würzburg
Emil-Fischer-Str. 30
97074 Würzburg, Germany
E-mail: advgeom@mathematik.uni-wuerzburg.de

Michael Joswig
Institut für Mathematik
Technische Universität Berlin
Sekretariat MA 6-2
Straße des 17. Juni 136
10623 Berlin, Germany

Editors

John Bamberg
Centre for the Mathematics of Symmetry and Computation
The University of Western Australia (M019)
35 Stirling Highway
Crawley, WA 6009, Australia

Eiichi Bannai
Faculty of Mathematics
Kyushu University
744, Motooka, Nishi-ku,
Fukuoka, Japan 819-0395

Renzo Cavalieri
Department of Mathematics
Colorado State University
Fort Collins, CO 80523-1874, USA

Izzet Coskun
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Chicago, IL 60607, USA

Patrick Eberlein
Department of Mathematics
University of North Carolina
CB 3250 Phillips Hall
Chapel Hill, NC 27599-3250, USA

Graziano Gentili
Dipartimento di Matematica
Universitá degli Studi di Firenze
Viale Morgagni, 67/a
50134 Firenze, Italy

Martin Henk
Institut für Mathematik
Technische Universität Berlin
Sekretariat MA 4-1
Straße des 17. Juni 136
10623 Berlin, Germany

William M. Kantor
Department of Mathematics
University of Oregon
Eugene, OR 97403-1222, USA

Gábor Korchmáros
Dipartimento di Matematica
Università degli Studi della Basilicata
Via Nazario Sauro 85
85100 Potenza, Italy

Alexander Kreuzer
Fachbereich Mathematik
Universität Hamburg
Bundesstr. 55
20146 Hamburg, Germany

Jeffrey C. Lagarias
Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor, Michigan 48109-1043, USA

Thomas Leistner
School of Mathematical Sciences
The University of Adelaide
Adelaide SA 5005, Australia

Rainer Löwen
Institut fur Analysis/Topologie
TU Braunschweig
Pockelsstr. 14
38106 Braunschweig, Germany

Kaoru Ono
Research Institute for Mathematical Sciences
Kyoto University
Kyoto, 606-8502 Japan

Daniel Plaumann
Fakultät für Mathematik
Technische Universität Dortmund
Vogelpothsweg 87
44227 Dortmund, Germany

Francisco Santos
Departamento de Matemáticas, Estadística y Computación
Universidad de Cantabria
Av. de los Castros 48
39005 Santander, Spain

Steven H. Weintraub
Department of Mathematics
Lehigh University
Bethlehem, PA 18015-3174, USA

Richard Weiss
Department of Mathematics
Tufts University
503 Boston Avenue
Medford, MA 02155, USA

Technical Editor

Nils Rosehr
Institut für Mathematik
Universität Würzburg
Emil-Fischer-Str. 30
97074 Würzburg, Germany

(Deutsch)

Online ISSN: 1615-7168
Print ISSN: 1615-715X
Type: Journal
Language: English
Publisher: De Gruyter
First published: March 1, 2001
Publication Frequency: 4 Issues per Year
Audience: Researchers in the field of geometry