Algebraic Geometry

Scope & Guideline

Bridging Concepts: Where Algebra Meets Geometry

Introduction

Welcome to the Algebraic Geometry information hub, where our guidelines provide a wealth of knowledge about the journal’s focus and academic contributions. This page includes an extensive look at the aims and scope of Algebraic Geometry, highlighting trending and emerging areas of study. We also examine declining topics to offer insight into academic interest shifts. Our curated list of highly cited topics and recent publications is part of our effort to guide scholars, using these guidelines to stay ahead in their research endeavors.
LanguageEnglish
ISSN2313-1691
PublisherEUROPEAN MATHEMATICAL SOC-EMS
Support Open AccessYes
CountryGermany
TypeJournal
Convergefrom 2014 to 2024
AbbreviationALGEBRAIC GEOM / Algebraic Geom.
Frequency6 issues/year
Time To First Decision-
Time To Acceptance-
Acceptance Rate-
Home Page-
AddressPUBLISHING HOUSE GMBH INST MATHEMATIK TECHNISCHE UNIV BERLIN STRASSE 17, JUNI 136, BERLIN 10623, GERMANY

Aims and Scopes

The journal 'Algebraic Geometry' serves as a leading platform for the dissemination of high-quality research in the field of algebraic geometry, focusing on both classical and contemporary topics. Its scope encompasses a wide range of themes, methodologies, and theoretical advancements, contributing significantly to the mathematical community.
  1. Classical Algebraic Geometry:
    Explores traditional topics such as curves, surfaces, and higher-dimensional varieties, often employing techniques from intersection theory and cohomology.
  2. Moduli Spaces and Stability Conditions:
    Investigates the structure and properties of moduli spaces, including stability conditions for various geometric objects, crucial for understanding deformation theory and compactifications.
  3. Homological Methods:
    Utilizes homological algebra techniques to address problems in algebraic geometry, including derived categories, sheaves, and cohomological invariants.
  4. Arithmetic Geometry:
    Focuses on the interplay between algebraic geometry and number theory, covering topics such as rational points, Fano varieties, and Diophantine geometry.
  5. Geometric Representation Theory:
    Examines the connections between algebraic geometry and representation theory, particularly in the context of geometric invariant theory and moduli problems.
  6. Singularity Theory and Resolutions:
    Studies singularities in algebraic varieties, including resolution techniques and their implications for birational geometry.
  7. Motivic and Tropical Geometry:
    Explores modern approaches to algebraic geometry through motivic integration and tropical geometry, emphasizing their applications in enumerative geometry.
The journal 'Algebraic Geometry' has seen a rise in innovative themes that reflect the evolving landscape of the field. Recent publications indicate a growing interest in the following areas, suggesting potential future directions for research.
  1. Mixed Characteristic Geometry:
    Recent works have emphasized the study of algebraic varieties in mixed characteristic, bridging classical algebraic geometry with modern number theory and arithmetic geometry.
  2. Homotopy and Derived Categories:
    There is a notable increase in the application of homotopical methods and derived categories, highlighting a trend towards more abstract and categorical approaches to classical problems.
  3. Geometric Invariant Theory:
    Emerging themes in geometric invariant theory are gaining traction, particularly in relation to moduli problems and the study of automorphisms of varieties.
  4. Tropical and Non-Archimedean Geometry:
    A growing interest in tropical geometry and non-Archimedean methods is evident, as these topics offer new perspectives and tools for addressing classical questions in algebraic geometry.
  5. Higher-Dimensional Varieties and Their Properties:
    Research focusing on higher-dimensional varieties, particularly Fano varieties and their properties, is on the rise, reflecting a shift towards understanding more complex geometric structures.
  6. Applications of Motivic Cohomology:
    The application of motivic cohomology to various problems in algebraic geometry is increasingly popular, indicating a trend towards integrating motives with classical geometry.

Declining or Waning

While 'Algebraic Geometry' has shown growth in various areas, certain traditional themes appear to be waning in prominence. The following scopes have seen a decline in recent publications, reflecting a shift in focus within the journal.
  1. Classical Techniques in Algebraic Geometry:
    There is a noticeable decrease in papers utilizing classical techniques such as projective geometry and classical intersection theory, as researchers increasingly explore more modern frameworks and tools.
  2. Local Cohomology and Local Properties:
    Research focusing on local cohomological techniques and local properties of varieties has become less frequent, possibly due to a broader interest in global properties and derived categories.
  3. Rationality Problems:
    While rationality remains a core topic, specific rationality problems related to lower-dimensional varieties have seen reduced attention, as the focus shifts to broader applications and higher-dimensional contexts.
  4. Special Varieties and Their Classifications:
    The classification of special types of varieties, such as specific classes of Fano varieties, appears to be less explored, possibly due to the increasing complexity of the subject and a pivot towards more general theories.

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