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Log structures, semistable degenerations, log crystalline cohomology, log de Rham cohomology, log smoothness, log Gromov-Witten theory
2
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Equivalence between $\bar{\mathcal{M}}_{g,n}$ and ${\mathcal{M}}_{g,n}^{logbas}$
It is a classical result of the theory of the moduli of curves, that the stack $\bar{\mathcal{M}}_{g,n}$ of nodal curves with log-structure coming from the boundary divisor, and ${\mathcal{M}}_{g,n}^{ …
2
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0
answers
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Tangent Space of Moduli of Log-Smooth Curves
We consider an algebraically closed field $\underline{k}$ and all constructions that we will consider are over this field. It is well known that for each relative nodal curve $\underline{f}: \underlin …
1
vote
0
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Cokernel of map of dual of sheaves of differentials/deformations
Let $C$ be a nodal projective curve over an algebraically closed field of genus at least $2$. There are two natural "differential objects" one can consider: The sheaf of differentials $\Omega_C$ and t …