SYZYGY
Financiado
Syzygies moduli and topological invariants of groups
This is a proposal aimed at harvesting interconnections between algebraic geometry and geometric group theory using syzygies. The impetus of the proposal is the recent breakthrough in which, inspired by rational homotopy theory, w...
This is a proposal aimed at harvesting interconnections between algebraic geometry and geometric group theory using syzygies. The impetus of the proposal is the recent breakthrough in which, inspired by rational homotopy theory, we introduced Koszul modules as novel homological objects establishing striking connections between algebraic geometry and geometric group theory. Deep statements in geometric group theory have startling counterparts in algebraic geometry and these connection led to a recent proof of Green's Conjecture for generic algebraic curves in arbitrary characteristic, as well as to a dramatically simpler proof in characteristic zero. Based on a dynamic view of mathematics in which ideas from one field trigger major developments in another, I propose to lead a group at HU Berlin dedicated to the following major themes, which are outlined in the proposal: (i) Find a solution to Green's Conjecture on the syzygies of an arbitrary smooth canonical curve of genus g. Find a full solution to the Prym-Green Conjecture on the syzygies of a general paracanonical algebraic curve of genus g. Formulate and prove a non-commutative Green's Conjecture for super algebraic curves. (ii) Compute the Kodaira dimension of the moduli space of curves in the transition case from unirationality to general type, when g is between 17 and 21. Construct the canonical model of the moduli space of curves and find its modular interpretation. (iii) Find algebro-geometric interpretations for Alexander invariants of the Torelli group of the mapping class group and that of the Torelli group of the free group. Understand the link between these invariants, the homotopy type and the cohomological dimension of the moduli space of curves. (iv) Get structural insight in the newly discovered topological version of Green's Conjecture involving the Alexander invariant of the group.
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Duración del proyecto: 90 meses
Fecha Inicio: 2019-06-25
Fecha Fin: 2026-12-31
Fecha Fin: 2026-12-31
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2019-06-25
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2018-ADG:
ERC Advanced Grant
Cerrada
hace 6 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
HUMBOLDTUNIVERSITAET ZU BERLIN
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
382.95K€ |
Participante