Recently, Jablonski proved that, to a large extent, simply connected solvable Lie group endowed with left-invariant Ricci soliton metric can be isometrically embedded into the Iwasawa of non-compact symmetric space. Motivated by this result, we classify codimension one subgroups groups irreducible spaces type whose induced metrics are solitons. We also obtain classifications Damek-Ricci and gen...

We study the generic tropical initial ideals of a positively graded Cohen-Macaulay algebra R over an algebraically closed field k. Building on work Römer and Schmitz, we give formula for each ideal, express associated quasivaluations in terms certain I-adic filtrations. As corollary, show that case is domain, every ideal coming from codimension 1 skeleton variety prime, so “generic presentation...