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bio website math.berkeley.edu/~vivek
location Berkeley, CA
age 31
visits member for 4 years, 8 months
seen 7 hours ago

Nov
12
comment Białynicki-Birula theory for non-complete varieties
see Bialynicki-Birula decomposition of a non-singular quasi-projective scheme.
Nov
11
answered Optimal definition of “paving by affine spaces”?
Nov
6
comment why are motives more serious than “naive” motives?
I wish this question was tripartide: there are also the original Chow motives, and I'd like to know where they fit in visavis the above analogies.
Nov
3
comment Can monodromy be described by the same matrix for chosen generators in case of the same singularity type?
the description of which loops you've chosen has an ambiguity the size of a braid group
Oct
24
comment Computing Euler Charactistics of Line bundles on Hilbert Schemes of points on Surfaces
Using that stuff for this computation would be utterly absurd. The Hilbert scheme of two points is just the blowup of the diagonal of the symmetric product, which should give you an explicit handle on all the classes you need for RR.
Oct
23
awarded  Popular Question
Sep
28
awarded  Great Answer
Sep
15
comment If the direct image of f preserves coherent sheaves on noetherian schemes, how to show f is proper?
why should it even be separated? the map from the affine line with the doubled origin to the affine line seems like it ought to preserve coherent sheaves
Sep
14
comment What are the exact holomorphic Lagrangians in complex 2-space?
@JasonStarr, sure, but those are all pretty similar to the zero section.
Sep
14
asked What are the exact holomorphic Lagrangians in complex 2-space?
Sep
10
accepted curve through a point avoiding an hypersurface, II
Sep
10
asked curve through a point avoiding an hypersurface, II
Sep
8
revised Singular points of algebraic varieties and parametrization by Puiseux series
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Sep
8
revised Singular points of algebraic varieties and parametrization by Puiseux series
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Sep
8
comment Singular points of algebraic varieties and parametrization by Puiseux series
About the higher order coefficients: without the requirement that $\gamma$ converge and certainly without the requirement that $\gamma(1)=q$, there's a name for such spaces -- they are called arc spaces, and are heavily studied as invariants of singularities. I think they can be pretty complicated; what you're asking is for is a linear condition on the subspace of convergent arcs, which sounds at least as complicated.
Sep
8
answered Singular points of algebraic varieties and parametrization by Puiseux series
Sep
8
revised Linearization instability and singular points of algebraic varieties
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Sep
8
comment Singular points of algebraic varieties and parametrization by Puiseux series
yeah, I just wanted to point out that you can't literally cut to a plane curve, since I at least find plane curves are easier to think about.
Sep
8
comment Singular points of algebraic varieties and parametrization by Puiseux series
Suppose $x,y \ne 0, 1$. Then by nondegeneracy of the Vandermonde determinant, any remaining point $(w, w^2, w^3, z, z^2, z^3)$ must have $(w, z) \in \{0,1,x\} \times \{0,1,y\}$. If $x = 0, 1$, then in fact $(w,w^2,w^3)$ has to be a scalar multiple of $(1,1,1)$; this only happens $w = 0, 1$. Thus in any case your plane hits $V$ in at most 9 points and in particular contains no curves.
Sep
8
comment Singular points of algebraic varieties and parametrization by Puiseux series
Why should such a plane exist? Strictly speaking, taking $V$ to be a non-planar curve is already a counterexample. If that's cheating, consider the product of two rational normal cubics, i.e. the variety which is the image in $\mathbb{C}^6$ of $\mathbb{C}^2$ by the map $(s,t) \mapsto (t, t^2, t^3, s, s^2, s^3)$. Say I take any plane through the points $p = (0,0,0,0,0,0)$ and $q = (1,1,1,1,1,1)$. Three points determine a plane; let $(x, x^2, x^3, y, y^2, y^3)$ be a third one.