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Results tagged with ag.algebraic-geometry
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user 128698
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
2
votes
1
answer
138
views
Extending isomorphism of family of pointed curve
Suppose that $(X,x)$ be pointed nonsingular curve and we have two families over $X$ of stable maps to$P^r$:
$(\pi:C\longrightarrow X,{p_i},f)$
($(\pi^{'}:C\longrightarrow X,{p_i}^{'},f^{'})$
If we …
- 71
2
votes
0
answers
212
views
Generalizing of normal sheaf via short exact sequence
I read in mirror symmetry and algebraic geometry by Cox and Katz that we have stable map $f : C \to Y$ which C is nodal curve with $n$ marked point then we have
$0 \to Ext^0_C([f^*\Omega_Y \to \Omega …
- 71
1
vote
0
answers
167
views
trace map for dualizing sheaf of nodal curves
In geometry of algebraic curve by Arbarello,Cornalba and Griffiths they difine trace map of dualizing sheaf of nodal curve as follows:
we choose $D=r_1 +r_2+...+r_h$ consisting of h distinct smooth …
- 71
1
vote
1
answer
292
views
exact sequence of deformations
Suppose that $C\cong P^1$ and $Def(f)$ denote the first order deformation of pointed stable map $(C,{p_i},f:C\longrightarrow X)$. I read that we have short exact sequence:
$0\longrightarrow H^0(C,T_C …
- 71
1
vote
0
answers
152
views
differential of stable map and boundry divisor
Suppose that $K=D(A;B;D_1;D_2)$ be a boundry divisor of $\overline{M}_{0,n}(X,\beta)$ and let $\overline{M}_A=$ $\overline{M}_{0,A \cup \bullet}(X,\beta)$ where $\bullet$ is additional marking.let $e_ …
- 71