论文信息 - Moduli of algebraic and tropical curves

Moduli of algebraic and tropical curves

Moduli spaces are a geometer’s obsession. A celebrated example in algebraic geometry is the space M g,n of stable n-pointed algebraic curves of genus g, due to Deligne—Mumford and Knudsen. It has a delightful combinatorial structure based on weighted graphs.

Dan Abramovich | D. Abramovich

[1] H. Hochstadt. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable; 3rd ed. (Lars V. Ahlfors) , 1980 .

[2] L. Ahlfors. Complex Analysis , 1979 .

[3] Grigory Mikhalkin. Tropical geometry and its applications , 2006 .

[4] G. Mikhalkin. Enumerative tropical algebraic geometry , 2003 .

[5] ENUMERATIVE TROPICAL ALGEBRAIC GEOMETRY IN R , 2004 .

[6] Margarida Melo,et al. On the tropical Torelli map , 2009, 0907.3324.

[7] Amaury Thuillier. Géométrie toroïdale et géométrie analytique non archimédienne. Application au type d’homotopie de certains schémas formels , 2007 .

[8] Sam Payne,et al. Nonarchimedean geometry, tropicalization, and metrics on curves , 2011, 1104.0320.

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

[10] Lucia Caporaso,et al. Algebraic and tropical curves: comparing their moduli spaces , 2011, 1101.4821.

[11] Filippo Viviani,et al. Tropicalizing vs Compactifying the Torelli morphism , 2012, 1204.3875.

[12] I. Tyomkin. Tropical geometry and correspondence theorems via toric stacks , 2010, 1001.1554.

[13] V. Berkovich. Spectral Theory and Analytic Geometry over Non-Archimedean Fields , 1990 .

[14] K. Vogtmann,et al. Moduli of graphs and automorphisms of free groups , 1986 .