EUR2023-143443
Financiado
Ciencias matemáticas
LEMUR TAKES PLACE AT THE INTERSECTION OF SINGULARITY THEORY, ALGEBRAIC GEOMETRY, AND COMMUTATIVE ALGEBRA. THIS PROJECT IS MOTIVATED BY THE DESIRE TO STRENGTHEN THE EXISTING CONNECTIONS BETWEEN LOCAL ALGEBRA AND ALGEBRAIC GEOMETRY:...
LEMUR TAKES PLACE AT THE INTERSECTION OF SINGULARITY THEORY, ALGEBRAIC GEOMETRY, AND COMMUTATIVE ALGEBRA. THIS PROJECT IS MOTIVATED BY THE DESIRE TO STRENGTHEN THE EXISTING CONNECTIONS BETWEEN LOCAL ALGEBRA AND ALGEBRAIC GEOMETRY: THE THEORY OF MODULI, MORIS MINIMAL MODEL PROGRAM, MUMFORDS GEOMETRIC INVARIANT THEORY, THE THEORY OF K-STABILITY. A FUNDAMENTAL PROBLEM IN ALGEBRAIC GEOMETRY IS TO FIND A CONVENIENT COMPACT MODULI SPACE THAT CONTAINS THE MODULI SPACE OF SMOOTH VARIETIES AS THIS ENABLES TO STUDY THE MODULI SPACE USING ALGEBRAIC GEOMETRY. MOTIVATED BY THE CLASS OF CURVES, THE VARIETIES PARAMETRISED BY A COMPACTIFICATION ARE CALLED STABLE. IN ORDER TO UNDERSTAND WHAT ARE STABLE VARIETIES, I.E., WHAT VARIETIES ARE LIMITS OF SMOOTH VARIETIES, IT IS NATURAL TO ASK WHAT SINGULARITIES ARE ALLOWED TO APPEAR ON STABLE VARIETIES.THESE COMPACTIFICATIONS CAN BE CONSTRUCTED IN DIFFERENT WAYS, SO THERE ARE DIFFERENT CLASSES OF STABLE VARIETIES. MUMFORDS APPROACH TO CONSTRUCTING THE MODULI WAS THE GEOMETRIC INVARIANT THEORY THAT HE CREATED AND HE GAVE A RESTRICTION, USING MULTIPLICITY THEORY, ON SINGULARITIES ON GIT-STABLE VARIETIES. LEMUR AIMS TO FURTHER MUMFORDS WORK: IT AIMS TO FURTHER DEVELOP THE MACHINERY OF LOCAL ALGEBRA ARISING FROM MUMFORDS WORK AND TO DEVELOP A BETTER UNDERSTANDING OF THE ALGEBRAIC PROPERTIES OF THE CLASS OF SINGULARITIES DEFINED BY MUMFORD. AS A LAST STEP, LEMUR HOPES TO EXPLORE THE PROPERTIES OF THE MULTIPLICITY THEORY ON SINGULARITIES ALLOWED BY THE TWO OTHER APPROACHES. SINGULARITIES\RESOLUTION OF SINGULARITIES.\DEFORMATIONS\LECHS INEQUALITY\MODULI SPACES\INTEGRAL CLOSURE\MULTIPLICITY THEORY
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Línea de financiación: concedida
El organismo AGENCIA ESTATAL DE INVESTIGACIÓN notifico la concesión del proyecto el día 2023-01-01
Presupuesto
El presupuesto total del proyecto asciende a
100K€
Líder del proyecto
BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
5M
Perfil tecnológico
TRL
4-5
5M