scholarly journals On the Kodaira Dimension of the Moduli Space of Curves

1982 ◽  
pp. 171-234 ◽  
Author(s):  
Joe Harris ◽  
David Mumford
Keyword(s):  
Moduli Space ◽  
Kodaira Dimension ◽  
Moduli Space Of Curves

The Kodaira dimension of the moduli space of curves of genus ?23

1987 ◽  
Vol 90 (2) ◽  
pp. 359-387 ◽  
Author(s):  
David Eisenbud ◽  
Joe Harris
Keyword(s):  
Moduli Space ◽  
Kodaira Dimension ◽  
Moduli Space Of Curves

scholarly journals On the Kodaira dimension of the moduli space of curves

1982 ◽  
Vol 67 (1) ◽  
pp. 23-86 ◽  
Author(s):  
Joe Harris ◽  
David Mumford
Keyword(s):  
Moduli Space ◽  
Kodaira Dimension ◽  
Moduli Space Of Curves

scholarly journals The Kodaira dimension of the moduli space of curves of genus {15}

1986 ◽  
Vol 24 (2) ◽  
pp. 205-220 ◽  
Author(s):  
Mei-Chu Chang ◽  
Ziv Ran
Keyword(s):  
Moduli Space ◽  
Kodaira Dimension ◽  
Moduli Space Of Curves

scholarly journals Kodaira dimension of moduli of special cubic fourfolds

2019 ◽  
Vol 2019 (752) ◽  
pp. 265-300 ◽  
Author(s):  
Sho Tanimoto ◽  
Anthony Várilly-Alvarado
Keyword(s):  
Complete Intersection ◽  
Cusp Form ◽  
Moduli Space ◽  
General Type ◽  
Kodaira Dimension ◽  
Countable Family ◽  
Prior Work ◽  
Low Weight ◽  
Modular Varieties ◽  
Cubic Fourfold

Abstract A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether–Lefschetz divisors {{\mathcal{C}}_{d}} in the moduli space {{\mathcal{C}}} of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties. We use the “low-weight cusp form trick” of Gritsenko, Hulek, and Sankaran to obtain information about the Kodaira dimension of {{\mathcal{C}}_{d}} . For example, if {d=6n+2} , then we show that {{\mathcal{C}}_{d}} is of general type for {n>18} , {n\notin\{20,21,25\}} ; it has nonnegative Kodaira dimension if {n>13} and {n\neq 15} . In combination with prior work of Hassett, Lai, and Nuer, our investigation leaves only twenty values of d for which no information on the Kodaira dimension of {{\mathcal{C}}_{d}} is known. We discuss some questions pertaining to the arithmetic of K3 surfaces raised by our results.

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