Relations in the Canonical Algebras on Surfaces

Konno, Kazuhiro

doi:10.4171/rsmup/120-13

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…This conjecture is still open although it is true for even surfaces with irregularity 0 ([28, Theorem 8.4]). According to [29], all even surfaces S with irregularity 0 satisfying the assumption of Conjecture 5.7 with K 2 S = 4p g (S) − 12 are classified into 5 classes. One of these classes consists of surfaces S that admit non-trigonal genus 5 fibrations f : S → P 1 with K 2 f = 4χ f .…”

Section: Applicationsmentioning

confidence: 99%

Upper bounds on the slope of certain fibered surfaces

Enokizono

2023

J. Math. Soc. Japan

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Using the theory of moduli of curves, we establish various slope inequalities for general fibered surfaces under the assumption that every fiber of the relative canonical model is reduced. To prove this, we introduce the notion of functorial divisors on Artin stacks and prove a theorem concerning their effectiveness. Furthermore, we consider the moduli stack of reduced and local complete intersection canonically polarized curves and prove that the closed substack parametrizing non-stable curves has no divisorial components. Applying the two theorems to effective tautological divisors on this moduli stack, we obtain several slope inequalities. As an application, we provide a positive partial answer to the question posed by Lu and Tan regarding the Chern invariants of fiber germs. Contents 1. Introduction 1 2. Intersection theory on Artin stacks 5 3. Moduli of curves 10 4. Boundary of moduli of reduced curves 13 5. Applications 18 Appendix A. A construction of moduli of curves 27 References 28

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Section: Applicationsmentioning

confidence: 99%

Upper bounds on the slope of certain fibered surfaces

Enokizono

2023

J. Math. Soc. Japan

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On the canonical ring of curves and surfaces

Franciosi

2012

manuscripta math.

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Let C be a curve (possibly non reduced or reducible) lying on a smooth algebraic\ud surface. We show that the canonical ring R(C, ωC) is generated in degree 1 if C is numerically four-connected, not hyperelliptic and even (i.e. with ω_C of even degree on every component).\ud As a corollary we show that on a smooth algebraic\ud surface of general type with pg(S) ≥ 1 and q(S) = 0 the canonical ring R(S, KS) is generated\ud in degree ≤ 3 if there exists a curve C ∈ |KS| numerically three-connected and not hyperelliptic

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Chain-connected component decomposition of curves on surfaces

Konno¹

2010

J. Math. Soc. Japan

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Relations in the Canonical Algebras on Surfaces

Cited by 3 publications

References 16 publications

Upper bounds on the slope of certain fibered surfaces

Upper bounds on the slope of certain fibered surfaces

On the canonical ring of curves and surfaces

Chain-connected component decomposition of curves on surfaces

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