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The hodge theory of algebraic maps

WebJul 21, 2014 · This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from … WebThis paper investigates the Hodge theory of proper algebraic maps f: X → Y of complex algebraic varieties and its topological implications. The key case is when X and Y are …

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WebMy current research focus is Hodge theory. Hodge theory associates to a family (or moduli space) of algebraic varieties a variation of Hodge structure, a.k.a. a period map. Period maps are powerful tools in the study of moduli spaces. The analysis of period maps involves both the geometry of the period domain (including curvature properties and ... WebAug 6, 2024 · Overview. Hodge theory is the study of properties of (complex, rational and integer) cohomology (and motives) of Kähler manifolds, induced by a Hodge filtration – given in the classical situation by harmonic differential forms – and the corresponding Hodge theorem.Hodge theory also applies in combinatorics, for instance to matroids ().. … manually manage music iphone https://mission-complete.org

The Hodge theory of algebraic maps - ScienceDirect

Webwhere [L]K is the K-theory signature of L. Extensions of Meyer’s formula to the singular setting were studied in [2] by means of intersection homology theory. In complex algebraic geometry, (twisted) signatures are just special cases of more general Hodge-type invariants. The purpose of this note is to announce Hodge the- WebHodge Theory of Maps Migliorini and de Cataldo June 24, 2010 1 Migliorini 1 - Hodge Theory of Maps The existence of a K ahler form give strong topological constraints via Hodge … WebThis map records, for each configuration B⊂ Cand for q= ζ−k d, the line in H 1(X)q ∼= Cr,s spanned by the holomorphic 1-form [dx/yk]. It is defined so long as 1/n kpdsb school cash online

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The hodge theory of algebraic maps

Hodge Theory and Moduli - albert.ias.edu

WebThe introductory lectures address Kahler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck's algebraic de Rham theorem. WebJul 21, 2014 · This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps.

The hodge theory of algebraic maps

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WebJun 2, 2003 · The Hodge theory of algebraic maps. Mark Andrea A. de Cataldo, Luca Migliorini. This paper investigates the Hodge theory of proper algebraic maps of complex … WebIn the talk the emphasis was on the relationship between Hodge theory and geometry, especially the study of algebraic cycles that was of such interest to Hodge. Special attention will be placed on the construction of geometric objects with Hodge-theoretic assumptions.

WebJul 31, 2024 · Building on the work of the fourth author in math.AG/9904074, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular … Expand. 406. PDF. Save. Alert. ... Hodge theory and complex algebraic geometry. C. Voisin, Leila Schneps; Mathematics. 2002; Introduction. … WebINTRODUCTION TO THE HODGE THEORY OF ALGEBRAIC VARIETIES 3 4. Hodge structures We define a Hodge structure of weight i to consist of a finitely generated Abelian group H ... is the unique Hodge structure of weight 2m. Given a map of compact oriented manifolds f : X → Y, recall there are maps ...

WebApr 29, 2015 · M. A. de Cataldo, L. Migliorini, The Hodge Theory of Algebraic maps, Ann. Scient. Éc. Norm. Sup., 4 e série, t. 38 , (2005), 693-750. M. A. de Cataldo, L. Migliorini, … WebJul 2, 2003 · TL;DR: The 2003 second volume of this account of Kaehlerian geometry and Hodge theory as discussed by the authors starts with the topology of families of algebraic varieties, and the main results of the second part are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly Nori's …

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complex algebraic varieties. The method rests on new Hodge-theoretic results on the cohomology …

Webrami cation of the j-function map C !M 1. A classical example of the use of IVHS is the theorem of Donagi-Green ([GMV]) concerning smooth hypersurfaces ... [V2]C. Voisin, … manually map driveWebFeb 4, 2016 · In its simplest form, Hodge theory is the study of periods - integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation … kpearce11 yahoo.com mailWebAbstract. This chapter summarizes the classical results of Hodge theory concerning algebraic maps. Hodge theory gives nontrivial restrictions on the topology of kpd to ypr train