Moduli Spaces associated with Singularities

Projektinformationen

ModSingLDT

ID Finanzhilfevereinbarung: 891437

DOI

10.3030/891437

Projekt abgeschlossen

EK-Unterschriftsdatum 31 August 2020

Startdatum 1 Januar 2021

Enddatum 31 Dezember 2022

Finanziert unter

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Gesamtkosten

€ 151 850,88

EU-Beitrag

€ 151 850,88

Koordiniert durch

HUN-REN RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Hungary

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

Berichtszeitraum: 2021-01-01 bis 2022-12-31

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

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.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

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.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

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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