We construct a new compactification of the moduli space Hg of smooth hyperelliptic curves of genus g. We compare our compactification with other well-known remarkable compactifications of Hg.

We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon. Connectedness and compactness are two fundamental topological properties. A natural question is whether a given space admits a connected (Hausdorff) compactification. This question has been st...

We study the one-loop dimensional crossover effects in six-dimensional orbifold compactifications of N=1 supersymmetric gauge theories. The behaviour of the one-loop effective beta function and of the 4D effective gauge coupling are analysed for a wide range of momentum scales k relative to the compactification scale(s). As k is increasing and approaching the compactification scale(s), there ex...

The countably-compactification of a topological space X is such its extension Y, that Y completely regular and countably-compact space, any closed subset in Y. But this does not always exist. Due to this, the concept saturation appeared, which generalisation countably-compactification: instead condition countably-compactness it necessary infinite has limit point Meanwhile, second remains unchan...

We give a definition of character sheaves on the group compactification which is equivalent to Lusztig’s definition in [Moscow Math. J. 4 (2004) 869-896]. We also prove some properties of the character sheaves on the group compactification.