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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Singular Algebraic Curves - With an Appendix by Oleg Viro (Hardcover, 1st ed. 2018)
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Singular Algebraic Curves - With an Appendix by Oleg Viro (Hardcover, 1st ed. 2018)
Series: Springer Monographs in Mathematics
Expected to ship within 12 - 19 working days
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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.
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