Singularities of 3-dimensional varieties admitting an ample effective divisor of Kodaira dimension zero

1996 ◽  
Vol 59 (4) ◽  
pp. 445-450 ◽  
Author(s):  
I. A. Cheltsov
Keyword(s):  
Kodaira Dimension ◽  
Effective Divisor ◽  
3 Dimensional ◽  
Dimension Zero

scholarly journals Two Moduli Spaces of Calabi–Yau type

2019 ◽  
Author(s):  
Ignacio Barros ◽  
Scott Mullane
Keyword(s):  
Moduli Spaces ◽  
K3 Surfaces ◽  
Kodaira Dimension ◽  
Effective Divisor ◽  
K3 Surface ◽  
Nodal Curve ◽  
Dimension Zero ◽  
M 10 ◽  
Lefschetz Pencils ◽  
Delta G

Abstract We show $\overline{\mathcal{M}}_{10, 10}$ and $\overline{\mathcal{F}}_{11,9}$ have Kodaira dimension zero. Our method relies on the construction of a number of curves via nodal Lefschetz pencils on blown-up $K3$ surfaces. The construction further yields that any effective divisor in $\overline{\mathcal{M}}_{g}$ with slope $<6+(12-\delta )/(g+1)$ must contain the locus of curves that are the normalization of a $\delta $-nodal curve lying on a $K3$ surface of genus $g+\delta $.

scholarly journals Halphen pencils on weighted Fano threefold hypersurfaces

2009 ◽  
Vol 7 (1) ◽  
pp. 1-45 ◽  
Author(s):  
Ivan Cheltsov ◽  
Jihun Park
Keyword(s):  
Kodaira Dimension ◽  
Dimension Zero ◽  
Fano Threefold

AbstractOn a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.

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