Moduli Spaces associated with Singularities

Informations projet

ModSingLDT

N° de convention de subvention: 891437

DOI

10.3030/891437

Projet clôturé

Date de signature de la CE 31 Août 2020

Date de début 1 Janvier 2021

Date de fin 31 Decembre 2022

Financé au titre de

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coût total

€ 151 850,88

Contribution de l’UE

€ 151 850,88

Coordonné par

HUN-REN RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Hungary

Periodic Reporting for period 1 - ModSingLDT (Moduli Spaces associated with Singularities)

Période du rapport: 2021-01-01 au 2022-12-31

Résumé du contexte et des objectifs généraux du projet

Moduli spaces are central objects of modern algebraic geometry. They have a strong relationship to natural enumerative questions. In many cases they are associated to a base variety and they contain a large amount of information about the geometry and topology of this base. In this project we investigated moduli spaces that were associated with singular spaces. These spaces have special points, or 'singularities', where the behavour of the space is different from what is expected. As our problems were in pure mathematics, our work is in general important for the wider scientific community including researchers in other areas such as theoretical physics or pure algebra. The main aim of the project was to find enumerative invariants of certain moduli spaces, for example Hilbert schemes and to obtain mathematical results on them.

Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent

The project proposed to contribute to enumerative invariants of the Hilbert schemes parametrizing zero-dimensional subschemes of some basic classes of surface singularities as well as of its analogues, and find connections between these enumerative invariants and vertex algebras. The project also made progress to the categorification of Heisenberg algebras and the quantum spectrum arising from Gromov-Witten invariants of surfaces.

Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)

We obtained several new and interesting results on Hilbert schemes and other moduli spaces. The research topic was at the meeting point of many different mathematical disciplines (such as enumerative algebraic geometry, mathematical physics, representation theory and so on). This interdisciplinary nature of the project makes it likely that the results will find their applications in various mathematical areas.

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