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Mixed hodge structures and singularities

By:

Kulikov, Valentine S

Series: Cambridge tracts in mathematics, no. 132Publication details: Cambridge University Press, 1998. Cambridge:Description: xxi, 186p.; hbk; 24cmISBN:

978052620604

DDC classification:

516.35 KUL

Summary: This 1998 book is both an introduction to, and a survey of, some topics of singularity theory; in particular the studying of singularities by means of differential forms. Here some ideas and notions that arose in global algebraic geometry, namely mixed Hodge structures and the theory of period maps, are developed in the local situation to study the case of isolated singularities of holomorphic functions. The author introduces the Gauss–Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure. This will be an excellent resource for all researchers whose interests lie in singularity theory, and algebraic or differential geometry. https://www.cambridge.org/core/books/mixed-hodge-structures-and-singularities/51C91E1A457EF98756F4ABCC60D59A22#fndtn-information

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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	516.35 KUL (Browse shelf(Opens below))	1	Available		031772

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Includes index and references

This 1998 book is both an introduction to, and a survey of, some topics of singularity theory; in particular the studying of singularities by means of differential forms. Here some ideas and notions that arose in global algebraic geometry, namely mixed Hodge structures and the theory of period maps, are developed in the local situation to study the case of isolated singularities of holomorphic functions. The author introduces the Gauss–Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure. This will be an excellent resource for all researchers whose interests lie in singularity theory, and algebraic or differential geometry.

https://www.cambridge.org/core/books/mixed-hodge-structures-and-singularities/51C91E1A457EF98756F4ABCC60D59A22#fndtn-information

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