MODULI SPACES OF ABELIAN SURFACES: COMPACTIFICATION, DEGENERATIONS, AND THETA FUNCTIONS (Expositions in Mathematics 12)

1995 ◽  
Vol 27 (5) ◽  
pp. 501-502
Author(s):  
G. K. Sankaran
Keyword(s):  
Moduli Spaces ◽  
Theta Functions ◽  
Abelian Surfaces

scholarly journals Factorization of Generalized Theta Functions Revisited

2017 ◽  
Vol 24 (01) ◽  
pp. 1-52
Author(s):  
Xiaotao Sun
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Theta Functions ◽  
Vanishing Theorems ◽  
Smooth Curves ◽  
Canonical Line Bundle

This survey is based on my lectures given in the last few years. As a reference, constructions of moduli spaces of parabolic sheaves and generalized parabolic sheaves are provided. By a refinement of the proof of vanishing theorems, we show, without using vanishing theorems, a new observation that [Formula: see text] is independent of all of the choices for any smooth curves. The estimate of various codimensions and computation of canonical line bundle of moduli space of generalized parabolic sheaves on a reducible curve are provided in Section 6, which is completely new.

scholarly journals Relative Proportionality for Subvarieties of Moduli Spaces of K3 and Abelian Surfaces

2009 ◽  
Vol 5 (3) ◽  
pp. 1161-1199 ◽  
Author(s):  
S. Mauller-Stach ◽  
E. Viehweg ◽  
K. Zuo
Keyword(s):  
Moduli Spaces ◽  
Abelian Surfaces

Conformal Blocks, Generalized Theta Functions and the Verlinde Formula

2021 ◽  
Author(s):  
Shrawan Kumar
Keyword(s):  
Graduate Students ◽  
Lie Algebras ◽  
Moduli Spaces ◽  
Theta Functions ◽  
Smooth Curve ◽  
Theoretical Physics ◽  
Affine Lie Algebras ◽  
Complete Proof ◽  
Conformal Blocks ◽  
Verlinde Formula

In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics.

scholarly journals Moduli spaces of the stable vector bundles over abelian surfaces

1980 ◽  
Vol 77 ◽  
pp. 47-60 ◽  
Author(s):  
Hiroshi Umemura
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Ample Line Bundle ◽  
Abelian Surfaces ◽  
Singular Variety ◽  
Stable Bundles ◽  
Stable Vector Bundles ◽  
Closed Subvariety

Let X be a projective non-singular variety and H an ample line bundle on X. The moduli space of H-stable vector bundles exists by Maruyama [4]. If X is a curve defined over C, the structure of the moduli space (or its compactification) M(X, d, r) of stable vector bundles of degree d and rank r on X is studied in detail. It is known that the variety M(X, d, r) is irreducible. Let L be a line bundle of degree d and let M(X, L, r) denote the closed subvariety of M(X, d, r) consisting of all the stable bundles E with det E = L.

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