Jeffrey D. Achter
Abstract
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Abstract Consider a finite morphismf:X→Yof smooth, projective varieties over a finite field . SupposeXis the vanishing locus in ℙNofrforms of degree at mostd. We show that there is a constantCdepending only on (N,r,d) and deg(f) such that if | | >C, thenf( ) :X( ) →Y( ) is injective if and only if it is surjective.
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Abstract Consider a finite morphismf:X→Yof smooth, projective varieties over a finite field . SupposeXis the vanishing locus in ℙNofrforms of degree at mostd. We show that there is a constantCdepending only on (N,r,d) and deg(f) such that if | | >C, thenf( ) :X( ) →Y( ) is injective if and only if it is surjective.
Key concepts: Mathematics, Injective function, Surjective function, Morphism, Locus (genetics), Pure mathematics, Combinatorics, Biochemistry