Moduli Spaces associated with Singularities

Información del proyecto

ModSingLDT

Identificador del acuerdo de subvención: 891437

DOI

10.3030/891437

Proyecto cerrado

Fecha de la firma de la CE 31 Agosto 2020

Fecha de inicio 1 Enero 2021

Fecha de finalización 31 Diciembre 2022

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 151 850,88

Aportación de la UE

€ 151 850,88

Coordinado por

HUN-REN RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Hungary

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

Período documentado: 2021-01-01 hasta 2022-12-31

Resumen del contexto y de los objetivos generales del proyecto

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.

Trabajo realizado desde el comienzo del proyecto hasta el final del período abarcado por el informe y los principales resultados hasta la fecha

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.

Avances que van más allá del estado de la técnica e impacto potencial esperado (incluida la repercusión socioeconómica y las implicaciones sociales más amplias del proyecto hasta la fecha)

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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