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9 votes
0 answers
286 views

derived schemes and perfect obstruction theories

In a survey article of Toen's it is claimed that that there is forgetful $\infty$-functor between the $\infty$-category of derived schemes locally of finite presentation over a field $k$ and the $\...
Fred's user avatar
  • 131
8 votes
1 answer
729 views

on a Deformation long exact sequence of moduli space of stable maps

I am reading the book "mirror symmetry" by Hori,Katz,Klemm,etc. And I want to understand the following Deformation long exact sequence \begin{align} 0 & \to Aut(Σ, p_1, . . . , p_n, f)\to Aut(Σ, ...
Xiaobo Zhuang's user avatar
4 votes
0 answers
248 views

Artin's "Versal Deformations and Algebraic stacks": Question concerning proof of Theorem 3.3

I have been reading Artin's paper titled "Versal deformations and algebraic stacks" and am a bit confused about a statement he makes in the proof of Theorem 3.3, in the first few lines of pg....
user's user avatar
  • 749
3 votes
0 answers
281 views

Vanishing of space of first order infinitesimal deformations for irreducible algebraic stack

This question has a few bits, and apologies if some questions are phrased poorly since I am not knowledgeable on the language of stacks or deformation theory. Suppose $\mathscr{X}$ is an algebraic ...
Daniel Levine's user avatar
1 vote
0 answers
119 views

Deformation theory about filtered sheaves

I am reading the paper “ Components of the stack of torsion-free sheaves of rank 2 on ruled surfaces” by C.Walter. In the proof of Lemma 4.1(a) ,in $Filtcoh(X)$ and an object $F_1 \subset F$ the ...
Walter field's user avatar