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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

1 vote
1 answer
1k views

General Orthogonal Group and its properties

I know that exist a Lie Group Called the Orthogonal Group $O(n)$. That correspond to all matrix of $n \times n$ in the real numbers such that the columns are a orthogonal basis for $\mathbb{R}^n$. Is …
Joaquín Moraga's user avatar
1 vote
0 answers
232 views

Is always a Crepant birational map between smooth varieties a small modification

Lemma: A crepant birational map between quasi-projective normal varieties with only terminal singularities is in fact small modifitacions, i.e. isomorphism in codimension 1. So, if $f:X\dashrightarro …
Joaquín Moraga's user avatar
2 votes
1 answer
472 views

Crepant Birational Map on the Blow-up

Let $ f: \mathbb{P}^n \dashrightarrow (\mathbb{P}^1)^n , [x_0:\dots :x_n] \mapsto ([x_0,x_1],[x_0,x_2], \dots ,[x_0,x_n])$ a birational map. In particular, if $X$ is the blow-up of $\mathbb{P}^n$ at …
Joaquín Moraga's user avatar
1 vote
1 answer
294 views

Crepant Birational Map

Let $ f: \mathbb{P}^n \dashrightarrow (\mathbb{P}^1)^n , [x_0:\dots :x_n] \mapsto ([x_0,x_1],[x_0,x_2], \dots ,[x_0,x_n])$ a birational map. Is $f$ a Crepant birational map?
Joaquín Moraga's user avatar
0 votes
3 answers
456 views

Zero-cohomology of birational varieties

Let $f:X\dashrightarrow Y$ be a birational map of smooth projective varieties, i.e., there exist open subsets $U_1, \subset X$ and $U_2 \subset Y$ such that $f|_{U_1} : U_1 \rightarrow U_2$ is an isom …
Joaquín Moraga's user avatar