03142nam 2200637 450 991078889870332120170816143318.01-4704-0689-6(CKB)3360000000464463(EBL)3113535(SSID)ssj0000888985(PQKBManifestationID)11539781(PQKBTitleCode)TC0000888985(PQKBWorkID)10875476(PQKB)10602583(MiAaPQ)EBC3113535(RPAM)2349617(PPN)195411617(EXLCZ)99336000000046446319830225h19831983 uy| 0engur|n|---|||||txtccrHodge theory and the local Torelli problem /Loring W. TuProvidence, Rhode Island :American Mathematical Society,[1983]©19831 online resource (72 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 279Includes index.0-8218-2279-9 Bibliography: pages 55-56.""Table of Contents""; ""Introduction""; ""I. Variation of Hodge structure""; ""Â1. The period map""; ""Â2. The Hodge bundles in the smooth case""; ""Â3. The Hodge bundles when there are singular fibers""; ""The log complex""; ""Relative dualizing sheaf""; ""The canonical extension""; ""Â4. A multiplicative formula for the holomorphic Euler characteristic""; ""Â5. Monodromy""; ""Â6. Mixed Hodge structures and the numerical invariants of a degeneration""; ""6.1. Varieties with normal crossings""; ""6.2. The limiting mixed Hodge structure""; ""6.3. The Clemensâ€?Schmid exact sequence""""6.4. Genus of a singular curve""""II. Local Torelli for curves""; ""Â7. The case of no singular fibers""; ""Â8. With singular fibers""; ""8.1. First proof: mixed Hodge structure and the topology of the singular fiber""; ""8.2. Second proof: using the relative dualizing sheaf to map X into a projective space""; ""8.3. Third proof: the ample cone on the moduli space M""; ""III. Local Torelli in higher dimensions""; ""Â9. Surfaces with large irregularity""; ""Â10. Threefolds and fourfolds with large irregularity""; ""Bibliography""; ""List of Notations""; ""Index""; ""A""; ""B""; ""C""""D""""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Y""Memoirs of the American Mathematical Society ;no. 279.Torelli problemCurves, AlgebraicSurfaces, AlgebraicHodge theoryTorelli theoremCurves, Algebraic.Surfaces, Algebraic.Hodge theory.Torelli theorem.510 s516.3/52Tu Loring W.52581MiAaPQMiAaPQMiAaPQBOOK9910788898703321Hodge theory and the local Torelli problem3799777UNINA