4,433 reputation
934
bio website nullteilerfrei.de
location Germany
age 29
visits member for 3 years, 8 months
seen 19 hours ago

I'm a PhD student with research interests in Algebraic Geometry, Algebraic Complexity Theory and Geometric Invariant Theory.


Sep
21
answered Can we say “commutative ring = field”?
Sep
20
asked Rational Points, classical versus modern notion
Sep
20
comment Is the maximal ideal of a localization at a prime ideal principal?
Also: A good place to read about this, in my opinion, is 11.1 of David Eisenbud's book Commutative Algebra with a View (Toward Algebraic Geometry).
Sep
20
revised Restriction of sheaf via inclusion induces isomorphism on stalks
added 17 characters in body
Sep
20
answered Restriction of sheaf via inclusion induces isomorphism on stalks
Sep
13
comment The greatest common divisor of homogeneous polynomials
If you choose $a_{ij}$ equal to the same polynomial $g$, the greatest common divisor of the $F_j$ will always be associated to $g$. Seems like this will heavily depend on the matrix $M$.
Sep
9
comment Local complete intersection ring
What is "the" maximal ideal of $R$? Is $R$ local or graded?
Sep
7
revised Two equivalent definitions of GIT semistable points
more tags
Aug
31
answered Sheaf associated to sheaf on basis
Aug
29
accepted Definition of multiplication in Grothendieck ring
Aug
29
comment Definition of multiplication in Grothendieck ring
Well, changing that $(-1)^i$ to $(-1)^{i-1}$ is pretty much the same as losing the Tor-zero term.
Aug
29
comment Definition of multiplication in Grothendieck ring
You should add Zhen Lin's comment to your answer: The problem is really that I treated $\mathscr G$ as part of the resolution. It is not enough to just start the sum at $1$, one needs to look at a different complext $\mathscr P_\bullet$ than I did.
Aug
29
comment Definition of multiplication in Grothendieck ring
@ZhenLin: Yea, I think I see now. I should replace $\mathscr P_0$ and $d_1$ by $0$ in my notation. I will get roughly the same, but will end up with $[\mathscr F]\cdot\sum_{i=1}^n (-1)^{i+1} [\mathscr R_i]$ which is precisely $[\mathscr F]\cdot[\mathscr G]$.
Aug
28
comment Definition of multiplication in Grothendieck ring
Hm. I actually thought about this? But starting the sum at $i=1$ doesn't seem to change anything, since $[\mathscr T_0]=[\mathscr K_0]-[\mathscr I_1]=[\mathscr P_0]-[\mathscr P_0]=0$ in my notation.
Aug
28
asked Definition of multiplication in Grothendieck ring
Aug
23
revised Maximal tori in $SO(n,\mathbb{C})$
edited tags
Aug
23
answered Maximal tori in $SO(n,\mathbb{C})$
Aug
15
comment Number of roots of two polynomials
@Tom: I am sorry, I am unfamiliar with that theorem, or at least with the name. What does it state?
Aug
14
revised Number of roots of two polynomials
added 16 characters in body
Aug
14
comment Number of roots of two polynomials
Dear @Tom, you still get the bound $\deg(f)\cdot\deg(g)$ which is sharp in general. In your example, you could conclude that there are at most $\max(d_1,d_2)^2$ many points in the intersection of the curves defined by $f$ and $g$.