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Tangent Conics at Quartic Surfaces and Conics in Quartic Double Solids
Author(s) -
Hadan Ingo
Publication year - 2000
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/(sici)1522-2616(200002)210:1<127::aid-mana127>3.0.co;2-c
Subject(s) - quartic function , conic section , monodromy , mathematics , tangent , fibered knot , quartic surface , space (punctuation) , pure mathematics , mathematical analysis , geometry , linguistics , philosophy
For a quartic double solid $Z \buildrel \varphi \over \longrightarrow P^3$ we study the parameter space of conics (i.e. of smooth rational curves C ⊂ Z such that C · φ* O P 3(1) = 2). This parameter space is naturally fibred (with disconnected fibres) over Pˇ 3 . We study the monodromy of the fibres and determine this way the irreducible components of the parameter space.