| 1. | The difficulties of algebraic geometry with passage to the quotient are acute.
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| 2. | Arithmetic geometry is an active field combining algebraic geometry and number theory.
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| 3. | For these reasons, projective space plays a fundamental role in algebraic geometry.
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| 4. | GW invariants can also be defined using the language of algebraic geometry.
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| 5. | This multiplicative inequality is useful in metric algebraic geometry and number theory.
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| 6. | In algebraic geometry, complex projective space is the home of algebraic varieties.
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| 7. | Modern algebraic geometry considers similar questions on a vastly more abstract level.
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| 8. | He is a specialist of model theory, number theory and algebraic geometry.
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| 9. | The fundamental objects of study in algebraic geometry are points at infinity.
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| 10. | Algebraic functions play an important role in mathematical analysis and algebraic geometry.
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