3,386 reputation
1022
bio website math.berkeley.edu/~achinger
location Berkeley
age 27
visits member for 4 years, 2 months
seen 2 hours ago
PhD student, UC Berkeley

Apr
16
revised Semiring of vector bundles on $\mathbb{C}\mathbb{P}^1$
deleted 143 characters in body
Apr
16
revised Semiring of vector bundles on $\mathbb{C}\mathbb{P}^1$
added 221 characters in body
Apr
16
comment Semiring of vector bundles on $\mathbb{C}\mathbb{P}^1$
right, I forgot I cannot subtract ;)
Apr
16
answered Semiring of vector bundles on $\mathbb{C}\mathbb{P}^1$
Apr
16
comment Semiring of vector bundles on $\mathbb{C}\mathbb{P}^1$
Very good question. Any element can be uniquely presented in the form $N$ or $N+MH^p$ with $p>0$. Multiplication and addition in this basis seems tricky though, e.g. $(2+3H^3)(4+5H^2) = 44 + H^{131}$ or something like that.
Apr
14
reviewed Approve suggested edit on The Alexander-Conway polynomial: from knots to braids?
Apr
14
comment Holomorphic trivialization of $(x,y) \subset \mathbb{C}[x,y]/(y^2 - x^3 + x)$
The question asked for a holomorphic, not algebraic, section. In the situation in question, the exponential sequence shows that since $H^1(X, O_X) = H^2(X, O_X) = 0$, we have $Pic(X) = H^2(X, \mathbb{Z})$, which is zero.
Apr
6
answered Existence of local sections
Mar
25
comment What is the combinatorial data classifying non-normal affine toric varieties?
(cont.) Note that any finite set of positive integers generates such a $P\subseteq \mathbb{N}$, but it's quite difficult to see whether two such sets generate the same monoid (see "Frobenius problem").
Mar
25
comment What is the combinatorial data classifying non-normal affine toric varieties?
Take a (rational polyhedral) cone $\sigma$ in $\mathbb{R}^n$ and remove a finite number of non-invertible elements of $P:=\sigma\cap \mathbb{Z}^n$. If the resulting $P'$ is a monoid (and if there are no invertible elements, you can make $P'$ a monoid by removing finitely many more elements), it gives you a non-normal affine toric variety, and all not necessarily normal affine toric varieties arise this way. I guess that pairs (cone, finite subset of integral points) is not what you're looking for. What answer would you like to have in case $P\subseteq \mathbb{N}$?
Mar
15
asked Can one prove that toric varieties are Cohen-Macaulay by finding a regular sequence?
Mar
10
awarded  Custodian
Mar
10
reviewed Approve suggested edit on Genus of Tutte-Coxeter Graph
Mar
8
revised Letter from Grothendieck to Tate on “crystals”
added tags
Mar
8
revised Deformation space form the point of view of intersection theory
added the ag.algebraic-geometry tag
Mar
4
comment local systems with cyclic monodromy
Given a connected cyclic cover $U'\to U$, you can normalize $X$ (a given compactification with snc boundary) in the fraction field of $U'$, yielding $p:X'\to X$. The multiplicities $\alpha_i$ come from ramification indices of $p$ along $D_i$. I guess you can find the line bundle $L$ in the $\mathbb{Z}/n$-decomposition of $p_* \mathcal{O}_{X'}$.
Mar
4
comment Does there exist a relative compactification with flat boundary?
Thank you for the useful reference! Do you believe this should be true for $S$ henselian and $X$ of higher dimension?
Mar
3
comment Order of the zero of a meromorphic function under the action of $Gal(\mathbb{C},\mathbb{Q})$
The map $X\to X^\sigma$ is an isomorphism of schemes (though not of $\mathbb{C}$-schemes). The order of vanishing of a function at a closed point does not depend on the structural morphism $\to Spec(\mathbb{C}$.
Mar
2
accepted Does there exist a relative compactification with flat boundary?
Mar
2
comment Does there exist a relative compactification with flat boundary?
Yes, I'm still interested in the case $S$ (strictly) Henselian.