Manuscript Topics

Algebraic geometry is a border area between geometry and algebra that enjoys great interest and projection in mathematical research. Specifically, in its most incipient beginnings, some decades ago, this rich area was concerned with the study of the geometric structures generated by the solutions of polynomial equations. Today, algebraic geometry extends its scope of interest to much more intricate geometric objects, from the most classical algebraic varieties to moduli spaces that parameterize bundles of all kinds on these same varieties. Likewise, the algebraic approach that characterizes its study allows us to carry out both geometric and topological investigations of the mentioned objects.

Today, algebraic geometry is an area of extraordinary interest to researchers, both from the point of view of pure mathematics and from the practical approach of its several mathematical, physical, and technical applications. Thus, from theoretical perspective, algebraic geometry contributes decisively to the understanding of a wide variety of geometric phenomena of great interest and relevance. Likewise, the implications derived from the deep interplay between pure algebraic geometry and its practical applications are at the forefront of geometric research.

This special issue considers research articles that provide novel, original, and high-quality contributions in the field of algebraic geometry, both from a theoretical perspective and from the approach of its practical applications. From a theoretical point of view, we welcome articles that delve into the structure and classification of moduli spaces, including vector and principal bundles, or Higgs bundles over curves or higher order varieties, and their subvarieties and automorphism groups. Submissions exploring intersection theory, stratifications of algebraic varieties or moduli spaces, geometric and topological aspects of algebraic curves and surfaces, derived categories, birational geometry, Hodge theory, and the geometry of higher-dimensional varieties are highly encouraged. On the applied front, we seek research that delves into implications of algebraic geometry in mathematical physics, dynamical systems, optimization, or data science.

We invite original research papers that address topics including, but not limited to:
• Moduli spaces of vector bundles, principal bundles and Higgs bundles
• Automorphisms of algebraic varieties and moduli spaces
• Intersection theory and enumerative geometry
• Stratifications and singularities of algebraic varieties
• Algebraic curves, surfaces, and higher-dimensional varieties
• Derived categories and birational geometry
• Hodge theory and cohomological methods
• Computational methods in algebraic geometry
• Applications of algebraic geometry to cryptography and coding theory
• Algebraic approaches in mathematical physics
• Applications of algebraic geometry to dynamical systems
• Algebraic-geometric approach to data science, machine learning, and optimization

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