A remark on the canonical degree of curves on smooth projective surface

2023/05/29 by Ciro Ciliberto, Ciliberto, Ciro, Claudio Fontanari +1
Arts and Humanities · Mathematics · Social Sciences · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #North African History and Literature #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2305.17923

openalex publication_date 2023/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The canonical degree C.K_X of an integral curve on a smooth projective surface X is conjecturally bounded from above by an expression of the form A(g-1)+B, where g is the geometric genus of C and A, B are constants depending only on X. We prove that this conjecture holds with A = -1 under the assumptions h⁰(X, -K_X) = 0 and h⁰(X, 2K_X + C) = 0.

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