Today’s Menu: Geometry and Resolution of Singular Algebraic Surfaces
نویسنده
چکیده
The courses are: Triviality, Tangency, Transversality, Symmetry, Simplicity, Singularity. These characteristic local plates serve as our invitation to algebraic surfaces and their resolution. Please take a seat.
منابع مشابه
Algebraic geometry and stability for integrable systems
In 1970s, a methodwas developed for integration of nonlinear equations bymeans of algebraic geometry. Starting froma Lax representationwith spectral parameter, the algebro-geometricmethod allows to solve the system explicitly in terms of theta functions of Riemann surfaces. However, the explicit formulas obtained in this way fail to answer qualitative questions such as whether a given singular ...
متن کاملFinite Branch Solutions to Painlevé Vi around a Fixed Singular Point * Dedicated to Professor Kazuo Okamoto on His Sixtieth Birthday
Every finite branch local solution to the sixth Painlevé equation around a fixed singular point is an algebraic branch solution. In particular a global solution is an algebraic solution if and only if it is finitely many-valued globally. The proof of this result relies on algebraic geometry of Painlevé VI, Riemann-Hilbert correspondence, geometry and dynamics on cubic surfaces, resolutions of K...
متن کاملA Tropical Approach to Enumerative Geometry
A detailed algebraic-geometric background is presented for the tropical approach to enumeration of singular curves on toric surfaces, which consists of reducing the enumeration of algebraic curves to that of non-Archimedean amoebas, the images of algebraic curves by a real-valued non-Archimedean valuation. This idea was proposed by Kontsevich and recently realized by Mikhalkin, who enumerated t...
متن کاملThe Geometry of Equisingular and Equianalytic Families of Curves on a Surface
Introduction The existence of singular algebraic curves with given invariants and given set of singular-ities and, at the same time, the study of (equisingular) families of such curves is a very old, but still attractive and widely open, problem. Already, at the beginning of the 20th century, the foundations were made in the works of Pl ucker, Severi, Segre and Zariski. In the sequel the theory...
متن کاملComputational Formal Resolution of Surfaces in Pc
In Algebraic Geometry smooth varieties are (in general) well-understood. By contrast (or simply because of that) the objects of interest are often singular varieties. From the theoretical point of view a remedy for this situation is the famous Theorem of Hironaka [8] on the resolution of singularities: If X is a variety over a field of characteristic 0 then there always exists a smooth variety ...
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تاریخ انتشار 2009