bio | website | math.berkeley.edu/~vivek |
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location | Berkeley, CA | |
age | 31 | |
visits | member for | 4 years, 8 months |
seen | 7 hours ago | |
stats | profile views | 3,515 |
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 |
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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 |
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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 |
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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
added 30 characters in body |
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 |
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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 |
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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. |