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Why do intersection of two quadratic forms implies elliptic curve?

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#algebraic-geometry
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Restriction maps in an integral scheme are injective

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#algebraic-geometry #schemes
85
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Show that $\mathbf{I}(\mathbf{V}(x^n, y^m)) = \langle x, y \rangle$.

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#algebraic-geometry
98
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What are some applications of parametrization of curves and surfaces?

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#number-theory #algebraic-geometry #algebraic-number-theory #surfaces #curves
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What are some elementary books which discuss projective lines on surfaces with examples?

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#algebraic-geometry #reference-request #surfaces #cubics #abelian-varieties
1.7k
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direct and inverse images of sheaves and some canonical morphisms

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#algebraic-geometry #sheaf-theory
163
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Is there a characterization of contractible hypersurfaces in $\mathbb{C}^2$.

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#algebraic-geometry #algebraic-topology #affine-geometry
827
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Cohomology of affine plane with double origin

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#algebraic-geometry
250
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Base change for Quot-scheme

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#algebraic-geometry #reference-request
132
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Minimal resolutions of singularities in higher dimensions and their cobordism class.

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#algebraic-geometry #algebraic-topology #singularity-theory
489
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Singular Points on Algebraic Curves

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#algebraic-geometry #definition #algebraic-curves
376
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Is there a classification of regular maps $\mathbb{P}^1(k)\to\mathbb{A}^1(k)$?

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#algebraic-geometry #reference-request
91
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How to calculate 2-d plane from 3 4-d points?

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#algebraic-geometry #recreational-mathematics
91
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Question related to the definition of affine schemes

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#algebraic-geometry #affine-schemes
116
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Evaluate a rational function at infinity

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#abstract-algebra #algebraic-geometry #cryptography

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