By Tohsuke Urabe

The learn of hypersurface quadrilateral singularities may be decreased to the research of elliptic K3 surfaces with a unique fiber of variety I * zero (superscript *, subscript 0), and for this reason those notes examine, along with the themes of the name, such K3 surfaces too. The combos of rational double issues which could ensue on fibers within the semi-universal deformations of quadrilateral singularities are tested, to teach that the attainable mixtures should be defined via a definite legislation from the point of view of Dynkin graphs. this is often resembling asserting that the attainable mixtures of singular fibers in elliptic K3 surfaces with a singular fiber of style I * zero (superscript *, subscript zero) should be defined through a undeniable legislation utilizing classical Dynkin graphs showing within the thought of semi-simple Lie teams. extra, the same description for thecombination of singularities on aircraft sextic curves is given. commonplace wisdom of algebraic geometry on the point of graduate scholars is anticipated. a brand new strategy in line with graphs will allure cognizance of researches.

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