Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Advanced Algebraic Geometry and Applications
share announcement

Advanced Algebraic Geometry and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 6929

Special Issue Editor

Dr. Francisco Javier Gallego

E-Mail Website
Guest Editor
Departamento de Álgebra, Geometría y Topología and Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain
Interests: algebraic geometry: projective equations and syzygies, vector bundles, projective surfaces and higher dimensional varieties, deformation theory of schemes and morphisms

Special Issue Information

Dear Colleagues,

Algebraic geometry is a classical, central area of mathematics, tracing its origins to many centuries ago. This discipline has evolved over the decades from many different approaches—algebraic, analytic, local, global, etc.—gaining depth, scope, and sophistication and building new or strengthening existing connections and imbrications with many other areas of mathematics, such as commutative algebra, computer algebra, number theory, differential geometry, complex analysis, topology, and mathematical physics, among others. At the same time, algebraic geometry has produced applications in several fields, such as cryptography, code theory, phylogenetics, integer programming, and statistics, to name just a few.

The aim of this Special Issue of Mathematics is to show a glimpse of all these different perspectives and flavors, from the most classical themes that should never become old-fashioned to the newest trends in the field. Thus, we cordially invite you to present your recent contributions to this Special Issue.

Dr. Francisco Javier Gallego
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • projective equations, free resolutions and syzygies
  • algebraic curves, moduli, Brill–Noether theory
  • surfaces and higher dimensional varieties, varieties of general type, moduli, Calabi–Yau manifolds
  • birational geometry
  • vector bundles
  • deformation theory of morphisms and schemes, fibrations, degenerations
  • subvarieties and subschemes of projective space
  • Grassmanians, homogeneous spaces

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (7 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

Jump to: Other

12 pages, 265 KiB  
Article
Multiplicities and Volumes of Filtrations
by Steven Dale Cutkosky
Mathematics 2025, 13(5), 694; https://doi.org/10.3390/math13050694 - 21 Feb 2025
Viewed by 297
Abstract
In this article, we survey some aspects of the theory of multiplicities of mR-primary ideals in a local ring (R,mR) and the extension of this theory to multiplicities of graded families of mR-primary ideals. [...] Read more.
In this article, we survey some aspects of the theory of multiplicities of mR-primary ideals in a local ring (R,mR) and the extension of this theory to multiplicities of graded families of mR-primary ideals. We first discuss the existence of multiplicities as a limit. Then, we focus on a theorem of Rees, characterizing when two mR-primary ideals I⊂J have the same multiplicity, and discuss extensions of this theorem to filtrations of mR-primary ideals. In the final sections, we give outlines of the proof of existence of the multiplicity of a graded family of mR-primary ideals as a limit, with mild conditions on R, and the proof of the extension of Rees’ theorem to divisorial filtrations. Full article
(This article belongs to the Special Issue Advanced Algebraic Geometry and Applications)
47 pages, 528 KiB  
Article
On (i)-Curves in Blowups of Pr
by Olivia Dumitrescu and Rick Miranda
Mathematics 2024, 12(24), 3952; https://doi.org/10.3390/math12243952 - 16 Dec 2024
Viewed by 611
Abstract
In this paper, we study (i)-curves with i∈{−1,0,1} in the blown-up projective space Pr in general points. The notion of (−1)-curves was analyzed in the early [...] Read more.
In this paper, we study (i)-curves with i∈{−1,0,1} in the blown-up projective space Pr in general points. The notion of (−1)-curves was analyzed in the early days of mirror symmetry by Kontsevich, with the motivation of counting curves on a Calabi–Yau threefold. In dimension two, Nagata studied planar (−1)-curves in order to construct a counterexample to Hilbert’s 14th problem. We introduce the notion of classes of (0)- and (1)-curves in Pr with s points blown up, and we prove that their number is finite if and only if the space is a Mori Dream Space. We further introduce a bilinear form on a space of curves and a unique symmetric Weyl-invariant class, F (which we will refer to as the anticanonical curve class). For Mori Dream Spaces, we prove that (−1)-curves can be defined arithmetically by the linear and quadratic invariants determined by the bilinear form. Moreover, (0)- and (1)-Weyl lines give the extremal rays for the cone of movable curves in Pr with r+3 points blown up. As an application, we use the technique of movable curves to reprove that if F2≤0 then Y is not a Mori Dream Space, and we propose to apply this technique to other spaces. Full article
(This article belongs to the Special Issue Advanced Algebraic Geometry and Applications)
8 pages, 250 KiB  
Article
The Assymptotic Invariants of a Fermat-Type Set of Points in P3
by Mikołaj Le Van and Tomasz Szemberg
Mathematics 2024, 12(24), 3945; https://doi.org/10.3390/math12243945 - 15 Dec 2024
Viewed by 525
Abstract
In this paper, we compute asymptotic invariants—specifically, the Waldschmidt constants and the Seshadri constants—of a set of 31 points in P3, defined as the intersection points of a Fermat-type arrangement of planes. Full article
(This article belongs to the Special Issue Advanced Algebraic Geometry and Applications)
14 pages, 277 KiB  
Article
Equivariant Holomorphic Hermitian Vector Bundles over a Projective Space
by Indranil Biswas and Francois-Xavier Machu
Mathematics 2024, 12(23), 3757; https://doi.org/10.3390/math12233757 - 28 Nov 2024
Viewed by 616
Abstract
The aim here is to describe all isomorphism classes of SU(n+1)-equivariant Hermitian holomorphic vector bundles on the complex projective space CPn. If G⊂SU(n+1) is the isotropy subgroup [...] Read more.
The aim here is to describe all isomorphism classes of SU(n+1)-equivariant Hermitian holomorphic vector bundles on the complex projective space CPn. If G⊂SU(n+1) is the isotropy subgroup of a chosen point x0∈CPn, and ρ:G⟶GL(V) is a unitary representation, we obtain SU(n+1)-equivariant holomorphic Hermitian vector bundles on CPn. Next, given any v∈End(Vρ)⊗(Tz00,1CPn)∗ satisfying certain conditions, a new structure of an SU(n+1)-equivariant holomorphic Hermitian vector bundle on this underlying C∞ holomorphic Hermitian bundle is obtained. It is shown that all SU(n+1)-equivariant holomorphic Hermitian vector bundles on CPn arise this way. Full article
(This article belongs to the Special Issue Advanced Algebraic Geometry and Applications)
13 pages, 297 KiB  
Article
Godeaux and Campedelli Surfaces via Deformations
by Haseeb Wali and Sohail Iqbal
Mathematics 2024, 12(19), 3123; https://doi.org/10.3390/math12193123 - 6 Oct 2024
Viewed by 729
Abstract
In this paper, we construct two deformations of the Godeaux surface with π1≅Z4, such that each central fibre contains a family of conics. We show that surfaces that are birational to these Godeaux surfaces exist in two connected [...] Read more.
In this paper, we construct two deformations of the Godeaux surface with π1≅Z4, such that each central fibre contains a family of conics. We show that surfaces that are birational to these Godeaux surfaces exist in two connected components of the moduli space of the Campedelli surfaces with a fundamental group of order 8. The whole construction is simplified by the use of key varieties. Full article
(This article belongs to the Special Issue Advanced Algebraic Geometry and Applications)
10 pages, 311 KiB  
Article
Hadamard Product of Monomial Ideals and the Hadamard Package
by Iman Bahmani Jafarloo, Cristiano Bocci and Elena Guardo
Mathematics 2024, 12(7), 1113; https://doi.org/10.3390/math12071113 - 8 Apr 2024
Viewed by 1697
Abstract
In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of [...] Read more.
In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and Sullivant. In the second part of the paper, we give a brief tutorial on the Hadamard.m2 package of Macaulay2. Full article
(This article belongs to the Special Issue Advanced Algebraic Geometry and Applications)

Other

Jump to: Research

9 pages, 240 KiB  
Systematic Review
A Survey on the Minimal Number of Singular Fibers of a P1-Semistable Curve
by Alexis G. Zamora
Mathematics 2024, 12(23), 3647; https://doi.org/10.3390/math12233647 - 21 Nov 2024
Viewed by 950
Abstract
Given a semistable and nonisotrivial fibered surface f:X→P1, this paper presents the main results on the problem of determining the minimal number of singular fibers that f must admit. The known examples of fibrations with a low [...] Read more.
Given a semistable and nonisotrivial fibered surface f:X→P1, this paper presents the main results on the problem of determining the minimal number of singular fibers that f must admit. The known examples of fibrations with a low number of singular fibers are presented. Some related problems are briefly discussed. Full article
(This article belongs to the Special Issue Advanced Algebraic Geometry and Applications)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-7
Back to TopTop