Complex geometry first appeared as a distinct area of study in the work of Bernhard Riemann in his study of Riemann surfaces. Comments: 24 pages, 7 figures. This is the second article in which we give a purely algebro-geometric proof of Verlinde formula. Recently, numerical algorithms have been developed for computing cell decompositions of the real points in complex algebraic curves and surfaces. Ask Question Asked 10 years ago. Are there applications of algebraic geometry into algebraic topology? Applicable Algebraic Geometry: Real Solutions, Applications, and Combinatorics Frank Sottile Summary While algebraic geometry is concerned with basic questions about solutions to equa-tions, its value to other disciplines is through concrete objects and computational tools, as applications require knowledge of specific geometric objects and explicit, often real-number, solutions. Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics.
These algorithms operate in the spirit of Morse theory by introducing a real projection and using numerical algebraic geometry to find the critical sets where the topology of the real fibers of the projection change. Complex geometry lies at the intersection of differential geometry, algebraic geometry, and analysis of several complex variables, and has found applications to string theory and mirror symmetry. Viewed 2k times 12.
It is said that the uses of cohomology, sheaves, spectral sequences etc. 7 $\begingroup$ It is described in many sources that algebraic topology had been a major source of innovation for algebraic geometry. Algebraic geometry emerged from analytic geometry after 1850 when topology, complex analysis, and algebra were used to study algebraic curves. Comments are welcomed. Subjects: Algebraic Geometry (math.AG); Combinatorics (math.CO); Representation Theory (math.RT) Comments: As suggested by a referee, we split arXiv:1802.08392 [math.AG] in two articles. Active 10 years ago. Well, yes if you allow “quantitative finance” to include modern models of economic behavior and decision making. Yes.