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

-1 votes
1 answer
500 views

Dominant morphism of Affine Scheme

Suppose to have $\phi$ a ring morphsim from $A$ to $B$, let $X=SpecA$ , $Y=SpecB$ and $\psi$ the induced morphism of affine schemes. It's true that if $\psi$ dominant than $\phi$ is injective?
1 vote
1 answer
2k views

the genus of a nonsingular projective curve is a birational invariant [closed]

Is true that two birational projectives nonsingular curves have the same genus? I know that for a non singular projective curve the genus is given by the formula 1/2(d-1)(d-2), where d is the degre …