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.
Algebraic varieties in Birkhoff strata of the Grassmannian Gr(2): Harrison cohomology and integrable systems
ORTENZI, GIOVANNI
2011-01-01
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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
