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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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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 …
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0
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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 …
2
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1
answer
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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 …
1
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1
answer
294
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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?
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3
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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 …