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Certain algebraic surfaces with Eisenbud‐Harris general fibration of genus 4
Author(s) -
Takahashi Tomokuni
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100304
Subject(s) - mathematics , fibration , quadric , twisted cubic , pure mathematics , algebraic curve , algebraic geometry , genus , elliptic curve , stable curve , algebraic number , projective space , algebraic surface , mathematical analysis , algebra over a field , projective line , homotopy , projective test , botany , biology
We classify the algebraic surfaces with Eisenbud‐Harris general fibration of genus 4 over a rational curve or an elliptic curve whose slope attains the lower bound. The classification of our surfaces is strongly related to the result of the classification for certain relative quadric hypersurfaces in 3‐dimensional projective space bundles over a rational curve and an elliptic curve. We further prove some results about the canonical maps, the quadric hulls of the canonical images and the deformation for these surfaces.