LEADER 00000nam a2200469 i 4500
001 978-3-030-03350-7
003 DE-He213
005 20190510151841.0
006 m o d
007 cr nn 008maaau
008 181230s2018 gw s 0 eng d
020 9783030033507|q(electronic bk.)
020 9783030033491|q(paper)
024 7 10.1007/978-3-030-03350-7|2doi
040 GP|cGP|erda
041 0 eng
050 4 QA565
082 04 516.352|223
100 1 Greuel, Gert-Martin,|eauthor
245 10 Singular algebraic cartinurves :|bwith an appendix by Oleg
Viro /|cby Gert-Martin Greuel, Christoph Lossen, Eugenii
Shustin
264 1 Cham :|bSpringer International Publishing :|bImprint:
Springer,|c2018
300 1 online resource (xx, 553 pages) :|billustrations,
digital ;|c24 cm
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
347 text file|bPDF|2rda
490 1 Springer monographs in mathematics,|x1439-7382
505 0 Zero-Dimensional Schemes for Singularities -- Global
Deformation Theory -- H 1-Vanishing Theorems --
Equisingular Families of Curves
520 Singular algebraic curves have been in the focus of study
in algebraic geometry from the very beginning, and till
now remain a subject of an active research related to many
modern developments in algebraic geometry, symplectic
geometry, and tropical geometry. The monograph suggests a
unified approach to the geometry of singular algebraic
curves on algebraic surfaces and their families, which
applies to arbitrary singularities, allows one to treat
all main questions concerning the geometry of equisingular
families of curves, and, finally, leads to results which
can be viewed as the best possible in a reasonable sense.
Various methods of the cohomology vanishing theory as well
as the patchworking construction with its modifications
will be of a special interest for experts in algebraic
geometry and singularity theory. The introductory chapters
on zero-dimensional schemes and global deformation theory
can well serve as a material for special courses and
seminars for graduate and post-graduate students.Geometry
in general plays a leading role in modern mathematics, and
algebraic geometry is the most advanced area of research
in geometry. In turn, algebraic curves for more than one
century have been the central subject of algebraic
geometry both in fundamental theoretic questions and in
applications to other fields of mathematics and
mathematical physics. Particularly, the local and global
study of singular algebraic curves involves a variety of
methods and deep ideas from geometry, analysis, algebra,
combinatorics and suggests a number of hard classical and
newly appeared problems which inspire further development
in this research area
650 0 Curves, Algebraic
650 14 Algebraic Geometry
700 1 Lossen, Christoph,|eauthor
700 1 Shustin, Eugenii,|eauthor
710 2 SpringerLink (Online service)
773 0 |tSpringer eBooks
830 0 Springer monographs in mathematics
856 40 |uhttps://doi.org/10.1007/978-3-030-03350-7