The local properties of the families of algebraic subsets Wg in the Birkhoff strata 2g of Gr(2) containing the hyperelliptic curves of genus g are studied. It is shown that the tangent spaces Tg for Wg are isomorphic to the linear spaces of 2-coboundaries. Particular subsets in Wg are described by the integrable dispersionless coupled KdV systems of hydrodynamical type defining a special class of 2-cocycles and 2-coboundaries in Tg. It is demonstrated that the blows-ups of such 2-cocycles and 2-coboundaries and gradient catastrophes for associated integrable systems are interrelated. © 2011 IOP Publishing Ltd.
Konopelchenko, B., Ortenzi, G. (2011). Algebraic varieties in Birkhoff strata of the Grassmannian Gr(2): Harrison cohomology and integrable systems. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 44 [10.1088/1751-8113/44/46/465201].
Algebraic varieties in Birkhoff strata of the Grassmannian Gr(2): Harrison cohomology and integrable systems
ORTENZI, GIOVANNIUltimo
2011
Abstract
The local properties of the families of algebraic subsets Wg in the Birkhoff strata 2g of Gr(2) containing the hyperelliptic curves of genus g are studied. It is shown that the tangent spaces Tg for Wg are isomorphic to the linear spaces of 2-coboundaries. Particular subsets in Wg are described by the integrable dispersionless coupled KdV systems of hydrodynamical type defining a special class of 2-cocycles and 2-coboundaries in Tg. It is demonstrated that the blows-ups of such 2-cocycles and 2-coboundaries and gradient catastrophes for associated integrable systems are interrelated. © 2011 IOP Publishing Ltd.
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