Stable maps and stable quotients

We analyze the relationship between two compactifications of the moduli space of maps from curves to a Grassmannian: the Kontsevich moduli space of stable maps and the Marian--Oprea--Pandharipande moduli space of stable quotients. We construct a moduli space which dominates both the moduli space of stable maps to a Grassmannian and the moduli space of stable quotients, and equip our moduli space with a virtual fundamental class. We relate the virtual fundamental classes of all three moduli spaces using the virtual push-forward formula. This gives a new proof of a theorem of Marian-Oprea-Pandharipande: that enumerative invariants defined as intersection numbers in the stable quotient moduli space coincide with Gromov--Witten invariants.Comment: 29 page

Leaders Role Within Cultural Industries

In the increasingly turbulent and competitive environment business, the dilemmas experienced by managers in cultural industries are characteristic to this type of industries where knowledge and creativity are key to sustaining competitive advantage. Firms that compete in cultural industries must deal with a combination of ambiguity and dynamism, both of which are intrinsic to goods that serve an aesthetic or expressive rather than a utilitarian purpose. This article develops the importance of leadership and its utility in the field of cultural industries. In order to meet the goals and to achieve the objectives within cultural industries we have proposed three leaders’ profiles which can offer a competitive advantage on the market. We describe major advances and emerging patterns in this research domain where managing act refers to key challenges leaders and is related to the extent to which leaders are inclined to take business-related risks (the risk-taking dimension), to favor change and innovation to obtain a competitive advantage for their organization (the innovation dimension), and to compete aggressively with other companies on the market (the proactiveness dimension).leader, management, cultural industries, competitive environment business.