Project description
A unified mathematical approach to calculating numerical invariants and line bundles
Investigating numerical invariants such as F-signatures and diagonal F-thresholds has recently revealed surprising links between commutative algebra and algebraic geometry. Supported by the Marie Skłodowska-Curie Actions programme, the PrIMes project will combine these notions with seemingly independent tools, including the cohomology of line bundles and the Lefschetz property. One of the main goals will be to establish recursive formulas for the multiplication of the Han-Monsky ring. The derived results will help classify the weak Lefschetz property in multi-variable monomial complete intersections. Furthermore, PrIMes will aim at studying these invariants for square-free hypersurfaces with the aid of combinatorial structures.
Objective
The study of numerical invariants in characteristic p, such as the F-threshold, diagonal F-threshold, and F-signature, is closely related to the theory of F-singularities and has recently attracted growing attention in both commutative algebra and algebraic geometry. Unexpected connections have emerged between these invariants and other topics of independent interest, such as the cohomology of line bundles on flag varieties, the Han-Monsky representation ring, and the Lefschetz property in positive characteristic.
This project aims to investigate these connections in depth, with the goal of achieving a comprehensive understanding of the Han-Monsky representation ring and using this knowledge to advance the study of invariants in characteristic p and the Weak Lefschetz Property.
On one hand, the Fellow will focus on invariants in positive characteristic, with the objective of computing the diagonal F-threshold for classes of square-free hypersurfaces with underlying combinatorial structure. In particular, attention will be given to the cone over the Grassmannian Gr(2,4) and to hypersurfaces defined by spanning tree polynomials.
In parallel, the researcher will study the graded Han-Monsky ring, aiming to prove a recursive formula for its multiplication in characteristic p>0. This result will then be applied to classify the Weak Lefschetz Property for monomial complete intersections in three or more variables.
The two directions will eventually converge in the final research objective: use the Han-Monsky framework to refine the understanding of the F-signature of Fermat hypersurfaces. More broadly, this aims to establish a methodology for advancing the study of invariants such as the F-signature and the diagonal F-threshold.
PrIMes will be hosted by the Università degli Studi di Genova and CIMAT (Mexico), leveraging the different expertise of the Supervisors and the Fellow to ensure the success of the goals of the Action.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics algebra commutative algebra
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics arithmetics prime numbers
- natural sciences mathematics pure mathematics algebra algebraic geometry
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-GF - HORIZON TMA MSCA Postdoctoral Fellowships - Global Fellowships
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2025-PF
See all projects funded under this callCoordinator
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
16126 GENOVA
Italy
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.