Hodge theory singularities and d-modules

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August undefined, 2024

Nettet1. jan. 1977 · As shown by J. Steenbrink [Ste77,Ste22], the homology group H m−1 carries a mixed Hodge structure, compatible with the monodromy. In the case of quasi-homogeneous isolated singularities, the ... Nettet11 – 15 April 2024. The goal of the conference is to give an account of the state of the art in the theory of D-modules and its applications. Emphasis will be put on results …

Hodge Theory - USTC

NettetD-modules are just W 1[x 1]-modules, and for any 2C we have the D-module x := W 1[x 1]=W 1[x 1](x@ ): Notice that the C[x;x 1]-module underlying x is free of rank one, i.e. the trivial line bundle, and the D-module structure is the at connection determined by r1 = x: Under the Riemann-Hilbert correspondence x is sent to L , where = e2ˇi . Nettetdiscuss the category of ltered D-modules, compatibility conditions with the V- ltration, and the inductive de nition of pure Hodge modules via vanishing/nearby cycles. We will … lewis and clark expedition landmarks

-modules - IHES

NettetISOMONODROMY, STABILITY, AND HODGE THEORY 5 Proof. The restriction (F,r)j C from Theorem 1.3.2 provides a semisimple ﬂat vector bundle; by Theorem 1.3.2(2), its isomonodromic deformation to a ... on C with regular singularities along D and irreducible monodromy. Suppose (E0,r0) is an isomonodromic deformation of (E,r) to a general … Nettetfocus are objects called Hodge ideals, intimately linked to Saito’s Hodge ltration on the D-module of functions with poles along a given divisor. They are a useful tool in studying … Nettetsection homology. With Shi-Wei-Shu we had a mini-seminar on D-modules, discussing the Bernstein polynomial. And of course, Deligne was there, the founder of mixed Hodge theory, and John Morgan, who extended this theory to homotopy groups. On hindsight one can say that all ingredients of mixed Hodge modules were present at the time. lewis and clark expedition start and end

Hodge theory meets the minimal model program: a survey of log …

HODGE THEORY - Harvard University

NettetAbstract. It is well known that numerical quantities arising from the theory of D-modules are related to invariants of singularities in birational geometry. This paper surveys a … Nettet25. mai 2016 · We use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal … mccloy john coxswain chief boatswain\u0027s matehttp://www-personal.umich.edu/~mmustata/DmodulesNotes_0330.pdf lewis and clark expedition timeline answers

"NettetWe consider a mixed Hodge moduleM on a normal surface sin- gularity (X;x) and a holomorphic function germ f :( X;x)! (C; 0). For the case that M has an abelian local monodromy group, we give a formula for the spectral pairs of f with values inM. This result is applied to generalize the Sebastiani-Thom formula and to describe the behaviour of … " - Hodge theory singularities and d-modules

Hodge theory singularities and d-modules

Spectral Pairs, Mixed Hodge Modules, and Series of Plane Curve ...

NettetThe purpose of these notes is to review how the Mixed Hodge Modules theory leads to an algebraic de nition of multiplier ideals in terms of D-modules, to a relation with … NettetI X is either smooth or has canonical singularities I X has given numerical characters K2 X;q(X);p g(X): Usually one says given ˜(O X), but as we are interested in Hodge theory we use q(X), p g(X). IThen it is known that there is a good moduli theory. (General reference: Koll ar, Moduli of varieties of general type, Handbook of Moduli, Vol. II ...

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NettetThe Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields.. The Fields Medal is regarded as one of the … Nettetare essentially two parts: vanishing and dimension results, for which Hodge modules are crucially needed, and linearity results, which apply to certain Hodge modules, but for which the general theory of D-modules and the harmonic theory of at line bundles su ce in the proofs. The theory of mixed Hodge modules is reviewed in x5 below.

NettetWe deal with the following specific topics: vanishing cohomology of isolated and non-isolated singularities. Rational homotopy generalisations of Hodge Theory and … Nettet1. jan. 2007 · Request PDF HODGE THEORY SINGULARITIES AND D-MODULES These notes, which consist of five lectures, intend to explain the notion of a polarized …

NettetThere are two versions of characteristic classes associated to mixed Hodge modules, cf. [5, 39]. The K-theoretical classes, called Hodge-Chern classes, capture information … Nettet5. mar. 2014 · HODGE THEORY SINGULARITIES AND D-MODULES. Article. Jan 2007; Claude Sabbah; These notes, which consist of five lectures, intend to explain the notion of a polarized Hodge D-module, ...

Nettet19. mar. 2014 · HODGE THEORY SINGULARITIES AND D-MODULES. Article. Jan 2007; Claude Sabbah; These notes, which consist of five lectures, intend to explain the notion of a polarized Hodge D-module, ...

Nettethodge theory, singularities and d-modules - GDR Singularites et ... EN English Deutsch Français Español Português Italiano Român Nederlands Latina Dansk Svenska Norsk … mccloy kitchens cullybackeyNettet7. jun. 2024 · This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various ... mccloy killyleaghNettetRegular holonomic D-modules ←→Perverse sheaves Applications. At the moment, there are no direct applications of the decom-position theorem for semisimple perverse sheaves (or holonomic D-modules). For instance, we are lacking numerical invariants to get numerical consequences (in Hodge theory, one would have the Hodge numbers). mccloy + muchemwa addresshttp://grupo.us.es/gfqm218/CIRM/curso-sabbah.pdf lewis and clark expedition timeline eventsNettetHodge structure on the vanishing cycles purely in terms of local properties of thesingularity. Atthispoint,thereisnomoreneedtodescendtotheparameter space(thedisc). … lewis and clark expedition st. louisNettetI am a Professor in the Department of Mathematics at University of Michigan.Here is my contact information. My work is in algebraic geometry. Over the past few years I have been involved in a long-term project with Mihnea Popa, studying certain invariants of hypersurface singularities (Hodge ideals) that arise naturally from Saito's theory of … mccloy kitchensNettetHodge theory meets the minimal model program: a survey of log canonical and Du Bois singularities SANDOR J. KOV´ ACS AND KARL E. SCHWEDE´ ABSTRACT. We … lewis and clark experience