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 
264  1 Cham :|bSpringer International Publishing :|bImprint: 
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