Giulio
  • Member for 7 years, 10 months
  • Last seen more than a week ago
Finite generation of certain graded sequences of ideals
0 votes

The best (algebraic) advice I can give is to look at section 2.2.5 of https://arxiv.org/pdf/1812.03538.pdf ( Uniqueness of K-polystable degenerations of Fano varieties by Blum and Xu) (eventually, ...

View answer
Connected sum of algebraic curves, handlebody decomposition, and induction on genus
2 votes

First, glue two points, obtaining a singular curve of genus $g_1+g_2$. Then smooth out the singularity. Equivalently, remove two discs, one from each curves, and glue two small annuli around the discs ...

View answer
Non-flat seesaw
Accepted answer
0 votes

I have received the following great answer from Vlad Lazić: In the numerical setup, what you ask (with some assumptions on the base, such as Q-factoriality) is well-understood, see the paper of ...

View answer
Pull-back of polarization
Accepted answer
1 votes

Yes! This is sometime called naturality of Chern classes. You can find it in many books, for instance Complex Geometry - An Introduction | Daniel Huybrechts, or Differential forms in algebraic ...

View answer
Tweetable Mathematics
4 votes

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

View answer
Cohomologies of double covers
1 votes

Yes! It follows from the fact that $$ d\pi \circ d\theta=d\pi $$ whihc in turn follows from $\pi\circ \theta=\pi$. I think you actually have an equality $H^2(X,\mathbb{Z})^{\theta}=\pi^*H^2(Y,\mathbb{...

View answer
Extending the tangent bundle of a submanifold
3 votes

Let us discuss first the differntial geometry case. Here, you can use the tubular neighbourhood theorem to extend the vector bundle. Explicitly, you have a neighbourhood $U$ of $Y$ in $X$ which is ...

View answer
References request: vector representations of Lie superalgebras
Accepted answer
1 votes

See for instance Manin, Yuri I. Gauge field theory and complex geometry or Quantum Fields and Strings: A Course for Mathematicians

View answer
Uniqueness of a (weighted) affine cone
Accepted answer
5 votes

Abotu the first question: yes, it does. Already for $\mathbb{P}^n$ embedded with $\mathcal{O}(d)$, the cone changes with $d$. About the second, you might view a cone as a variety with a $\mathbb{G}_m$...

View answer
Normality via resolution of singularities
1 votes

This should be true: let $X=Spec(B)$ and $Y=Spec(A)$ be Noetherian affine schemes, if $$ f\colon X\to Y $$ is faithfully flat and $X$ is normal, then $Y$ is normal. A proof is given in Corollary 15.4 ...

View answer
Representation Theory of Lie Groups: Reference Request
2 votes

I like the book by Claudio Procesi Lie Groups: An Approach through Invariants and Representations

View answer
Quasicoherent sheaves on superschemes
Accepted answer
3 votes

Some basic references are: the book by Manin Gauge Field Theory and Complex Geometry ; the first paper by Delinge in Quantum Fields and Strings: A Course for Mathematicians ; the recent paper on the ...

View answer
What is the cohomology of the tangent bundle of a flag variety?
Accepted answer
2 votes

The answer might be in Michel Demazure. Automorphismes et déformations des variétés de Borel. Invent. Math., 39(2):179–186, 1977

View answer
Soft question: beginners reference to moduli spaces
6 votes

The introductions of each chapter of Geometry of Algebraic Curves, Volume II, Arbarello Enrico, Cornalba Maurizio, Griffiths Phillip (the book itself is tuff, but the introductions are extremely ...

View answer
Sheaf of isogenies representable?
1 votes

It should be representable by an ind-scheme. You should look at the papere by Mumford "On the equations defining abelian varieties II", section 9. He calls this moduli space $\mathcal{M}_{\infty}$, it ...

View answer
Reference request: SGA7
1 votes

To start with: Galois Groups and Fundamental Groups, by Tamás Szamuely (The theorem in section 3.4 about the absolute Galois group go $\mathbb{C}(t)$ is amazing and enlightening.) And then: Milne, ...

View answer