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Log structures, semistable degenerations, log crystalline cohomology, log de Rham cohomology, log smoothness, log Gromov-Witten theory

2 votes
0 answers
113 views

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}^{ …
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2 votes
0 answers
93 views

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 …
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  • 223
1 vote
0 answers
110 views

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 …
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  • 223