# Classification of projective surfaces and projective normality

@article{Akahori1998ClassificationOP,
title={Classification of projective surfaces and projective normality},
author={Katsumi Akahori},
journal={Tsukuba journal of mathematics},
year={1998},
volume={22},
pages={213-225}
}
• K. Akahori
• Published 1 June 1998
• Mathematics
• Tsukuba journal of mathematics
8 Citations

### Normal generation and covers of small degree

• K. Akahori
• Mathematics
Communications in Algebra
• 2019
Abstract Let L be a special very ample line bundle of degree on a curve X with sufficiently high genus g. We show that L is normally generated if and X is not a sheeted covering of a curve.

### Remarks on normal generation of special line bundles on multiple coverings

Let L be a special very ample line bundle of degree $$\text{ deg }(L)$$deg(L) on a curve X with sufficiently high genus g. We prove that L is normally generated if \text{ deg }(L) \ge 2g-3-6h^1(L)

### Remarks on Normal Generation of Special Line Bundles on Algebraic Curves

Let L be a very ample line bundle with h 1(L) ≥2 on a curve of genus g. We prove that L is normally generated if deg(L) ≥2g − 1 − 4h 1(L) for large enough genus g.

### PROJECTIVE NORMALITY OF ALGEBRAIC CURVES AND ITS APPLICATION TO SURFACES

• Mathematics
• 2006
Let L be a very ample line bundle on a smooth curve C of genus g with (3g + 3) 2 deg L 2g 5. Then L is normally generated if deg L max 2g + 2 4h 1 (C, L), 2g (g 1) 6 2h 1 (C, L) . Let C be a triple

### Normal generation of line bundles of degree 2g - 1 - 2h1 (L) - Cliff(X) on curves

Let Cliff(X) be the Clifford index of a curve. We determine necessary and sufficient conditions for very ample line bundles of degree deg(L) = 2g - 1 -2h1(L) - Cliff(X) being not normally generated.

### Remarks on normal generation of line bundles on algebraic curves

We determine necessary and sufficient conditions for nonspecial line bundles of degree 2% - 4 and 2g - 5 being not normally generated. Furthermore, we also determine necessary and suffcient

### Title Projective normality of algebraic curves and itsapplication to surfaces

Let L be a very ample line bundle on a smooth curve C of genusg with (3g + 3)=2 < degL 2g 5. Then L is normally generated ifdegL > maxf2g + 2 4h1(C, L), 2g (g 1)=6 2h1(C, L)g. Let C be a triple