On the Kodaira dimension of Hurwitz spaces

The Kodaira Dimension of Certain Moduli Spaces of Abelian Surfaces

Moduli Spaces for polarized abelian surfaces are obtained as quotients of the Siegel upper half–plane H2 by arithmetic subgroups of the symplectic group Sp(4,Q). In this paper we will look at the Kodaira dimension of the moduli spaces At which parameterize abelian surfaces with a polarization of type (1, t). For many small values of t it is known that At is rational or unirational (e.g. see the...

The Kodaira Dimension of Spaces of Rational Curves on Low Degree Hypersurfaces

For a hypersurface in complex projective space, X ⊂ Pn, we investigate the singularities and Kodaira dimension of the Kontsevich moduli spacesM0,0(X, e) parametrizing rational curves of degree e on X. If d + e ≤ n and X is a general hypersurface of degree d, we prove thatM0,0(X, e) has only canonical singularities and we conjecture the same is true for the coarse moduli space M0,0(X, e). We pro...

On the Kodaira Dimension of the Moduli Space of Curves

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On the logarithmi Kodaira dimension of aÆne threefolds

Kodaira Dimension and Symplectic Sums

Modulo trivial exceptions, we show that symplectic sums of symplectic 4-manifolds along surfaces of positive genus are never rational or ruled, and we enumerate each case in which they have Kodaira dimension zero (i.e., are blowups of symplectic 4-manifolds with torsion canonical class). In particular, a symplectic four-manifold of Kodaira dimension zero arises by such a surgery only if it is d...