14,867 reputation
13377
bio website math.purdue.edu/~dvb
location
age
visits member for 4 years, 1 month
seen 8 hours ago

2d
comment What is the “complex third derivative”?
I don't have a good answer (I'm not an SCV guy), but (1) it has a coordinate free expression as you said (2) it specializes to (a constant times) the laplacian in 1 complex variable.
Apr
8
comment Smooth mixed hodge modules - representations of fundamental group?
The answer is pretty much what Sam & Dan are saying. While I don't want to self-advertise, you can take a look at front.math.ucdavis.edu/0902.4252 for a bit more info.
Apr
3
awarded  Nice Answer
Apr
2
answered Down-to-earth expositions of Hodge theory
Mar
31
answered Quillen's motivation of higher algebraic K-theory
Mar
27
awarded  Good Answer
Mar
26
comment Is there any advantage to knowing that Gauss-Manin is Hermitian flat?
My recollection is that Griffiths did notice this. I don't have time to check myself right now, but see his "Periods of integrals… III"
Mar
21
comment mixed Hodge structure on Cohomology with compact support
For the reasons explained in Dan's answer, $H^k_c(X)\cong H^{2n-k}(X)^*\otimes \mathbb{Q}(-n)$ as MHS. In general, the weights are compatible with what happens in etale cohomology (I'm not sure if that helps you).
Mar
20
revised When are two subvarieties of matrices conjugate?
added 1008 characters in body
Mar
19
answered When are two subvarieties of matrices conjugate?
Mar
15
comment Parabolic bundle and chern class
I'm not really sure why the reaction to this question is so negative. My guess is that the parabolic degree ought to be expressible as Chern-Weil integral for a suitably chosen metric on the restriction of the bundle to the open part. Some results along these lines can be found in papers of Biquard or T. Mochizuki.
Mar
9
awarded  Cleanup
Mar
9
revised Log forms and Tate classes
rolled back to a previous revision
Mar
8
revised Log forms and Tate classes
added 31 characters in body
Mar
8
answered Log forms and Tate classes
Mar
4
comment Blowdown and contraction
Your new Q2 should be fine. What sort of answer do you want for Q1?
Mar
3
awarded  Enlightened
Mar
3
awarded  Nice Answer
Mar
3
comment Blowdown and contraction
I think you have the wrong sign, very ample divisors are not (birationally) contractible.
Feb
28
revised Open subgroups of the etale fundamental group of $P^1_\mathbb Q\setminus\{0,\infty\}$
added 1 characters in body