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2d

comment 
Bott formula for projective bundles
I think a more close analogue is given by the formulas for relative differentials  $R^p\pi_*(\Omega^q_{P/B}) = \mathcal{O}_B$ for $p = q$ and $0$ otherwise. Then the formulas for the pushforwards of $\Omega^q_P$ can be obtained from (exterior powers) of the standard sequence $0 \to \pi^*\Omega_B \to \Omega_P \to \Omega_{P/B} \to 0$. 
2d

comment 
Bott formula for projective bundles
The analogue of Bott's formula computes the (derived) direct images of these sheaves to the base of the projective bundle. 
Apr 16 
comment 
Is any quadric birational to a product of BrauerSeveri varieties?
This is what I meant in the last sentence. 
Apr 16 
answered  Is any quadric birational to a product of BrauerSeveri varieties? 
Apr 14 
answered  Holomorphic trivialization of $(x,y) \subset \mathbb{C}[x,y]/(y^2  x^3 + x)$ 
Apr 8 
comment 
Recognizing a Mukai flop
No, I want to say the following. Assume that $\mathcal{V} \cong \mathcal{V}^*$. Then the morphism $M \to \bar{M}$ (your initial data) satisfies all your assumptions for $M' \to \bar{M}$. But clearly it does not give you a flop. So, in a sense, the main problem is to distinguish between $M$ and $M'$. This is usually done (as Sandor explains) by considering additional divisor $D$ which is assumed to be positive for one morphism and negative for the other. 
Apr 2 
answered  Examples for curve not 1connected but $h^0(C, O_C)=1$ 
Mar 31 
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Why should noncommutative CYs be dgas?
This scholar.google.ru/… is a good reference. 
Mar 29 
answered  Why should noncommutative CYs be dgas? 
Mar 27 
comment 
Recognizing a Mukai flop
Imagine that the vector bundle $\mathcal{V}$ is selfdual. Then you can take $M' = M$, $\nu' = \nu$. But clearly this is NOT the flop. This shows that you definitely need an additional condition. 
Mar 17 
comment 
An ample line bundle on a K3 surface
It is. Take two divisors $D_1$ and $D_2$ in $O(1,1)$. Then $f^{1}(D_1) \cap f^{1}(D_2) = f^{1}(D_1 \cap D_2)$. 
Mar 17 
answered  An ample line bundle on a K3 surface 
Mar 15 
comment 
canonical bundle skewsymmetric determinantal varieties
Find a resolution and compute its canonical class  it will be a sum of a multiple of the pullback of a hyperplane on $P(\Lambda^2V)$ and a multiple of the exceptional divisor. The first summand is what you want. 
Mar 14 
comment 
a net of quadrics and the corresponding intersection
It does not matter how they meet. Still each time it is an ample divisor. 
Mar 13 
comment 
a net of quadrics and the corresponding intersection
Apply this 3 times. 
Mar 13 
answered  a net of quadrics and the corresponding intersection 
Mar 12 
revised 
Would such polynomial identity exist? (related to sum of four squares)
added 17 characters in body 
Mar 12 
comment 
Would such polynomial identity exist? (related to sum of four squares)
You are right, sorry. 
Mar 12 
answered  Would such polynomial identity exist? (related to sum of four squares) 
Mar 9 
comment 
Counting curves of degree 4 in $\mathbb{P}^{3}$
@Jeremy Blanc: you are right of course, it is much simpler to project the curve and do not care about the quadrics. 