Algebraic varieties in the Birkhoff strata of the Grassmannian Gr((2)): Harrison cohomology and integrable systems

作者：Konopelchenko B G^*; Ortenzi G

来源：Journal of Physics A-Mathematical and Theoretical, 2011, 44(46): 465201.

DOI：10.1088/1751-8113/44/46/465201

The local properties of the families of algebraic subsets W-g in the Birkhoff strata Sigma(2g) of Gr((2)) containing the hyperelliptic curves of genus g are studied. It is shown that the tangent spaces T-g for W-g are isomorphic to the linear spaces of 2-coboundaries. Particular subsets in W-g are described by the integrable dispersionless coupled KdV systems of hydrodynamical type defining a special class of 2-cocycles and 2-coboundaries in T-g. It is demonstrated that the blows-ups of such 2-cocycles and 2-coboundaries and gradient catastrophes for associated integrable systems are interrelated.

• 出版日期2011-11-18