bio  website  math.sunysb.edu/~jstarr/… 

location  Stony Brook University, Stony Brook, NY USA  
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2h

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Lie algebra of holomorphic vector fields
Just to point out: even considered as a module over the infinitedimensional algebra of holomorphic functions on the cotangent bundle, still the Lie algebra is not generated by $\mathfrak{g}$. In the case of the cotangent bundle of $\mathbb{P}^1$, the cokernel is onedimensional, generated by the vector field of "scaling" on the quadric cone. 
2h

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Lie algebra of holomorphic vector fields
The cotangent bundle of $\mathbb{P}^1$ is a minimal desingularization of the affine quadric surface cone (with a single ordinary double point), e.g., the quotient of the affine plane by the $1$action. The Lie algebra is infinitedimensional. In what terms do you want a description of this infinitedimensional Lie algebra? 
8h

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Integral domains equal to intersection of their height one localizations
A onedimensional, local, integral domain has this property. So there are many examples, e.g., the local ring of $k[x,y]/\langle y^2  x^3 \rangle$ at the maximal ideal $\langle x,y\rangle$. 
1d

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Non trivial rank 2 holomorphic vector bundles in complex dimensions greater than or equal 2
Oops, complex tori don't work: $h^{0,1}$ is always nonzero. 
1d

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Non trivial rank 2 holomorphic vector bundles in complex dimensions greater than or equal 2
Aren't complex tori Oka manifolds? 
Aug
27 
revised 
Construction of coherent sheaf such that $\text{Proj}\,\text{Sym}\,(\mathcal{F}) = \text{Sym}^n X$
added 367 characters in body 
Aug
27 
answered  Construction of coherent sheaf such that $\text{Proj}\,\text{Sym}\,(\mathcal{F}) = \text{Sym}^n X$ 
Aug
27 
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Construction of coherent sheaf such that $\text{Proj}\,\text{Sym}\,(\mathcal{F}) = \text{Sym}^n X$
I guess what you really need is a Poincare sheaf on $X\times \text{Pic}^nX$. Do you have a Poincare sheaf? If you have a zerocycle of degree $1$ on $X$, then you have a Poincare sheaf. 
Aug
27 
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Construction of coherent sheaf such that $\text{Proj}\,\text{Sym}\,(\mathcal{F}) = \text{Sym}^n X$
Every construction that I know requires choosing a rational point on $X$. Does your curve have a rational point? Does it at least have a zerocycle of degree $1$? 
Aug
27 
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Elementary examples on sheaf extension
Are you asking about $\text{Ext}^1_{\mathcal{O}_{C_V}}$, or are you asking about $\text{Ext}^1_{\mathcal{O}_{T*\mathbb{P}^n}}$? For the former, quite frequently the Ext group will be zero, e.g., when $V$ is any rational curve. However, for the latter, the group is nonzero already when $V$ is a line in $\mathbb{P}^2$. 
Aug
26 
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Derived pullback of the coarse moduli morphism
Both exactness of $f_*$ and $\theta$ being isomorphic can be checked etale locally on $X$. Thus, assume that $\mathcal{X}$ is $[Y/G]$ with induced map $F:Y\to X$ and $G$ prime to the characteristic. Then $f_*f^*$ is the same as $(F_*F^*())^G$. Since $F$ is finite (hence affine), $F_*$ is exact. Since $G$ is prime to the characteristic $()^G$ is exact. Thus $f_*$ is exact. Because $f_*$ is exact, to check $\theta$ is isomorphic, it suffices to consider $\theta_{\mathcal{O}}$. This case follows from the definition of the categorical quotient of $Y$ by $G$. 
Aug
26 
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Derived pullback of the coarse moduli morphism
Flatness of $f$ is a corollary of the local flatness criterion, cf. Theorem 23.1, p. 179 of H. Matsumura, Commutative Ring Theory, Cambridge U. Press. However, via the ChevalleyShephardTodd theorem, your hypotheses are extremely strong. 
Aug
26 
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Derived pullback of the coarse moduli morphism
First of all, in the tame case, $Rf_*$ equals $f_*$. In the nontame case, $Rf_*$ does not even map $D^b$ to $D^b$. 
Aug
26 
revised 
Derived pullback of the coarse moduli morphism
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Aug
26 
revised 
Derived pullback of the coarse moduli morphism
added 1 character in body 
Aug
26 
answered  Derived pullback of the coarse moduli morphism 
Aug
25 
answered  The cohomology ring of a compact toric manifold 
Aug
24 
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Annihilators of elements in symmetric algebras
@user43326. The map $M\to M\otimes_R M$ need not be injective. For instance, if $R$ is $\mathbb{Z}$ and $M$ is $\mathbb{Q}/\mathbb{Z}$, then the target module is the zero module, and the map is the zero map. 
Aug
24 
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Is the elementary transformation along a curve decomposable?
Just to expand on Mohan's comment: if the kernel is $u:E\to \mathcal{O}_S^{\oplus 2}$, what is the image of the induced homomorphism $\bigwedge^2 u: \bigwedge^2 E \to \mathcal{O}_S$? If $E$ is a direct sum of invertible sheaves $F\oplus G$, what does this imply about $F\otimes_{\mathcal{O}_S}G$? What does this, further, imply about the pushforward of $c_1(A)$ versus $c_1(F)\cdot c_1(G)$? 
Aug
24 
answered  Definition of Strongly Stable 0cycle 