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Mock Modularity at Work, or Black Holes in a Forest. [PDF]
Entropy (Basel)Alexandrov S.
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Computational Methods and Function Theory, 2007
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1980
In this section we introduce the crucial concept of stability of holomorphic vector bundles over ℙ n . We begin by collecting together several theorems about torsion-free, normal and reflexive sheaves which we shall need later. Then we define stable and semistable torsion-free sheaves in the sense of Mumford and Takemoto and compare this concept of ...
Christian Okonek +2 more
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In this section we introduce the crucial concept of stability of holomorphic vector bundles over ℙ n . We begin by collecting together several theorems about torsion-free, normal and reflexive sheaves which we shall need later. Then we define stable and semistable torsion-free sheaves in the sense of Mumford and Takemoto and compare this concept of ...
Christian Okonek +2 more
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ON COMPACTIFICATIONS OF THE MODULI SPACE OF INSTANTONS
International Journal of Mathematics, 1990An instanton is defined to be a self-dual SU(2)-connection on \(S^ 4\) and its Pontrjagin number is called the instanton number. Instantons with instanton number n have a real algebraic, connected moduli space I(n). Donaldson showed that if a natural topology is introduced to \(\coprod^{n}_{a=0}I(n-a)\times \Sigma^ a(S^ 4) \), then it is a ...
Maruyama, M., Trautmann, Günther
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2014
Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to an understanding of the objects themselves. First formalised in the 1960s, it represents a significant topic of modern mathematical research with strong connections to many areas of mathematics ...
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Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to an understanding of the objects themselves. First formalised in the 1960s, it represents a significant topic of modern mathematical research with strong connections to many areas of mathematics ...
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2017
This chapter focuses on the moduli space of Riemann surfaces. The moduli space parameterizes many different kinds of structures on Sɡ, such as isometry classes of hyperbolic structures on S, conformal classes of Riemannian metrics on S, biholomorphism classes of complex structures on S, and isomorphism classes of smooth algebraic curves homeomorphic to
Benson Farb, Dan Margalit
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This chapter focuses on the moduli space of Riemann surfaces. The moduli space parameterizes many different kinds of structures on Sɡ, such as isometry classes of hyperbolic structures on S, conformal classes of Riemannian metrics on S, biholomorphism classes of complex structures on S, and isomorphism classes of smooth algebraic curves homeomorphic to
Benson Farb, Dan Margalit
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ON THE SLOPES OF THE MODULI SPACES OF CURVES
International Journal of Mathematics, 1998On the moduli space \(\overline{\mathcal M}_g\) of stable complex curves of genus \(g\) one has the boundary divisors \(\Delta_i\) (\(i=0, \dots,[g/2]\)) and their classes \(\delta_i\) (\(i=0,2,3, \dots,[g/2]\)) and \(\delta_1=[\Delta_1]/2\). We write \(\delta=\delta_0+ \dots+\delta_{[g/2]}\) and \(\lambda\) for the class of the Hodge line bundle on ...
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Parameter Spaces and Moduli Spaces
1992We can now give a slightly expanded introduction to the notion of parameter space, introduced in Lecture 4 and discussed occasionally since. This is a fairly delicate subject, and one that is clearly best understood from the point of view of scheme theory, so that in some sense this discussion violates our basic principle of dealing only with topics ...
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