Hodge theory singularities and d-modules

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August undefined, 2024

NettetSingularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. Nettet1. feb. 2024 · For a smooth algebraic variety X, a monodromic D-module on X × ℂ is decomposed into a direct sum of some D-modules on X. We show that the Hodge …

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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 … totto y feid

hodge theory, singularities and d-modules - GDR Singularites et ...

NettetHodge 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 … 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. Nettethodge theory, singularities and d-modules - GDR Singularites et ... EN English Deutsch Français Español Português Italiano Român Nederlands Latina Dansk Svenska Norsk … pothys swarna mahal tirunelveli

(Open Access) An introduction to homological algebra (1960) D.

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

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. 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, ... tot toyNettet10. jan. 2024 · and well done. $\blacksquare$ Section 1.3. The Cone of Curves of Smooth Varieties. Definition 1.15. More properties of extremal faces and rays we refer chapter 18 (especially Theorem 18.5) in book [Convex97] 1 which is important for us to read the Mori’s theory. $\blacksquare$ Theorem 1.24. pothys swarna mahal website

"NettetRecent advances in Hodge theory, the theory of singular hermitian metrics and moduli theory of higher dimensional varieties have led to major breakthroughs in solving long-standing problmes in complex algebraic geometry, in particular birational geometry.. In Hodge theory, Saito’s theory of Hodge modules have proved to be a specially … " - Hodge theory singularities and d-modules

Hodge theory singularities and d-modules

Some examples of the Riemann-Hilbert correspondence

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 … 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 …

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Nettethodge theory, singularities and d-modules - GDR Singularites et Read more about hodge, projective, hypercohomology, singularities, global and variety. Nettet20. jun. 2024 · SFB/TRR 45 Summer School, July 9--13 2024, Mainz, Germany. This summer school is intended for advanced master students, PhD students, and younger researchers in algebraic geometry. The purpose is to familiarize the participants with techniques from Hodge Theory, in particular mixed Hodge modules, and their …

NettetBiography Alexandru Dimca. Alexandru Dimca obtained his PhD in 1981 from the University of Bucharest. His field of interest is the topology of algebraic varieties, singularities of spaces and maps, Hodge theory and D-modules. Dimca has been a visiting member of the Max Planck Institute in Bonn and the Institute for Advanced … 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 …

NettetHODGE THEORY, SINGULARITIES AND D-MODULES CLAUDE SABBAH Abstract. These notes, which consist of ﬁve lectures, intend to explain the notion of a polarized … NettetRegular 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).

NettetAn introduction to homological algebra. D. G. Northcott. 31 Dec 1959 -. TL;DR: In this paper, the authors propose a theory of homology and cohomology theories of groups and moniods, and derive derived functors from homology functors, including Tensor products, groups of homomorphisms, and projective and injective modules. Abstract: Preface 1.

NettetMorihiko Saito introduced the theory of Mixed Hodge Modules around 1985, which unifies many theories: algebraic D-modules and perverse sheaves. 2 Hodge structure A quick review of Hodge theory for real manifolds. Let (M,g) be a compact orientable Riemann manifold. For k 2 N, let Ωk(M) be the real vector space tot tracingNettetThe 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 … pothys swarna mahal trivandrumNettet1. 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 … tot trackerNettetMULTIPLIER IDEALS AND HODGE THEORY BY RADU DAN NERO BUDUR M.S., University of Illinois, Chicago, 1999 ... 3.1.2 D-modules and the Riemann-Hilbert correspondence . . . . 62 ... and measures in a subtle way the singularities of D. The singularities of Dget "worse" if J(D) is smaller. tot tqtNettetAlgebraic Geometry and Singularities - Jun 06 2024 The volume contains both general and research papers. Among the ﬁrst ones are papers showing recent and original developments or methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. tot toy organizerNettetThere are two versions of characteristic classes associated to mixed Hodge modules, cf. [5, 39]. The K-theoretical classes, called Hodge-Chern classes, capture information … tott playersNettet16. feb. 2024 · A generalization of Hodge theory to arbitrary complex algebraic varieties was developed by Deligne [17, 18].He showed that the cohomology of a complex algebraic variety (not necessarily complete or nonsingular) carries a slightly more general structure, which presents $H^k(X,\mathbb {C})$ as a successive extension of Hodge structures … tot training in istanbul turkey