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KODAIRA DIMENSION OF UNIVERSAL HOLOMORPHIC SYMPLECTIC VARIETIES
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 21 / Issue 6 / November 2022
- Published online by Cambridge University Press:
- 02 February 2021, pp. 1849-1866
- Print publication:
- November 2022
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- Article
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We prove that the Kodaira dimension of the n-fold universal family of lattice-polarised holomorphic symplectic varieties with dominant and generically finite period map stabilises to the moduli number when n is sufficiently large. Then we study the transition of Kodaira dimension explicitly, from negative to nonnegative, for known explicit families of polarised symplectic varieties. In particular, we determine the exact transition point in the Beauville–Donagi and Debarre–Voisin cases, where the Borcherds
$\Phi _{12}$
form plays a crucial role.
Universal Families of Rational Tropical Curves
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- Journal:
- Canadian Journal of Mathematics / Volume 65 / Issue 1 / 01 February 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 120-148
- Print publication:
- 01 February 2013
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We introduce the notion of families of
$n$-marked, smooth, rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical varieties into the moduli space of $n$-marked, abstract, rational, tropical curves 
${{\mathcal{M}}_{n}}$.
