Compactifications of the generalized Jacobian variety

The generalized Jacobian variety of an algebraic curve with at most ordinary double points is an extension of an abelian variety by an algebraic torus. Using the geometric invariant theory, we systematically compactify it in finitely many different ways and describe their structure in terms of torus embeddings. Our compactifications include all known good ones.

[1]  W. Haboush.  Reductive groups are geometrically reductive , 1975 .

[2]  Y. Namikawa.  A new compactification of the Siegel space and degeneration of Abelian varieties. II , 1976 .

[3]  M. Maruyama.  Stable vector bundles on an algebraic surface , 1975, Nagoya Mathematical Journal.

[4]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[5]  A. Ramanathan.  Stable principal bundles on a compact Riemann surface , 1975 .

[6]  D. Mumford,et al.  Geometric Invariant Theory , 2011 .

[7]  Frank Harary,et al.  Graph Theory , 2016 .

[8]  J. Igusa.  Fibre Systems of Jacobian Varieties: (II. Local Monodromy Groups of Fibre Systems) , 1956 .

[9]  D. Gieseker.  On the moduli of vector bundles on an algebraic surface , 1977 .

[10]  D. Mumford,et al.  The irreducibility of the space of curves of given genus , 1969 .

[11]  C. A. Rogers,et al.  Packing and Covering , 1964 .

[12]  David Mumford,et al.  Toroidal Embeddings I , 1973 .

[13]  D. Mumford.  An analytic construction of degenerating abelian varieties over complete rings , 1971 .

[14]  D. Mumford,et al.  Periods of a Moduli Space of Bundles on Curves , 1968 .

[15]  David Mumford,et al.  Curves and their Jacobians , 1975 .

[16]  T. J. Dickson.  On Voronoi reduction of positive definite quadratic forms , 1972 .

[17]  Allen Tannenbaum,et al.  Lectures on deformations of singularities , 1976 .

[18]  Michel Raynaud,et al.  Spécialisation du foncteur de Picard , 1970 .

[19]  P. Deligne,et al.  Les Schémas de Modules de Courbes Elliptiques , 1973 .

[20]  I. Nakamura.  On moduli of stable quasi abelian varieties , 1975, Nagoya Mathematical Journal.

[21]  S. Langton.  Valuative Criteria for Families of Vector Bundles on Algebraic Varieties , 1975 .

[22]  C. S. Seshadri,et al.  Stable and unitary vector bundles on a compact Riemann surface , 1965 .