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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 Brauer-Severi varieties?
This is what I meant in the last sentence.
Apr
16
answered Is any quadric birational to a product of Brauer-Severi 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 1-connected but $h^0(C, O_C)=1$
Mar
31
comment 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 self-dual. 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 skew-symmetric 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.