2,958 reputation
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bio website math.berkeley.edu/~vivek
location Berkeley, CA
age 31
visits member for 4 years, 6 months
seen yesterday

Sep
15
comment If the direct image of f preserves coherent sheaves on notherian 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.
Aug
31
comment Different definitions of linkless graphs
yes, those are clearly different definitions. however the distinction is irrelevant for the purposes of that second paper, since flat implies [KKM]-linkless implies [RST]-linkless implies, as shown in [RST], the existence of some flat embedding.
Aug
26
revised Twist in identification with singular cohomology
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Aug
25
revised Twist in identification with singular cohomology
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Aug
25
answered Twist in identification with singular cohomology
Aug
22
revised How do I find coefficients of a product expansion
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Aug
22
revised How do I find coefficients of a product expansion
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Aug
22
comment How do I find coefficients of a product expansion
I am vaguely aware that there's an answer to this question of the form ``take a logarithm and do symmetric function combinatorics'', but I wasn't able to reconstruct the details.