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Hartshorne Chapter 1 Exercise 7.7 (a)

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#algebraic-geometry #projective-varieties
92
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The definition for the morphism of varieties in Hartshorne's book.

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#algebraic-geometry #affine-varieties #projective-varieties
70
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lines passing through two points in $\mathbb{P}^n$

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#algebraic-geometry #projective-geometry #projection #projective-varieties
120
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About the definition of the morphisms of varieties in Hartshorne's algebraic geometry.

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#algebraic-geometry #commutative-algebra #affine-varieties #projective-varieties
34
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Smoothness of affine variety consisting of finitely many points

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#algebraic-geometry #affine-schemes #affine-varieties #projective-varieties
143
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Gluing two affine curves to make a smooth curve

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#algebraic-geometry #curves #elliptic-curves #arithmetic-geometry #projective-varieties
95
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Exercise 1.12 (c) of Silverman "The Arithmetic of Elliptic Curves"

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#algebraic-geometry #algebraic-curves #projective-varieties
154
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Applications of the Lefschetz Hyperplane Theoren

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#algebraic-geometry #algebraic-topology #hodge-theory #projective-varieties
92
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How to prove the image of the morphism $\varphi:C\to \mathbb{P}^1$ is dense in $\mathbb{P}^1$?

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#algebraic-geometry #projective-varieties
172
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Intuition behind equations of Segre variety

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#algebraic-geometry #projective-geometry #projective-varieties
146
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Complete Intersection of Hypersurfaces are Fano varieties

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#algebraic-geometry #intersection-theory #divisors-algebraic-geometry #projective-varieties
116
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Hausdorff dimension of an algebraic variety

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#measure-theory #algebraic-geometry #geometric-measure-theory #projective-varieties
197
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Does birational equivalence between varieties preserves dimensions?

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#algebraic-geometry #projective-varieties
64
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Is a nonconstant morphism of projective varieties necessarily finite?

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#algebraic-geometry #schemes #projective-varieties
72
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Generator of the maximal ideal of $\mathcal{O}_p$

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#algebraic-geometry #commutative-algebra #projective-varieties

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