2 00 1 Surfaces with p g = q = 2 and an irrational pencil
نویسنده
چکیده
We classify all the irrational pencils over the surfaces of general type with pg = q = 2; as a byproduct it gives an evidence for the Catanese conjecture on surfaces of general type with pg = q = 2.
منابع مشابه
On Surfaces with P G = 2, Q = 1 and Non-birational Bicanonical Map *
In the present note we show that any surface of general type over C with pg = 2,q = 1 and non birational bicanonical map has a pencil of curves of genus 2. Combining this result with previous ones, one obtains that an irregular surface S of general type with χ(S) ≥ 2 and non-birational bicanonical map has a pencil of curves of genus 2.
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In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general type S with pg = q = 1 having an involution i such that S/i is a non-ruled surface and such that the bicanonical map of S is not composed with i. A complete list of possibilities is given and several new examples are constructed, as bidouble covers of surf...
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The present paper is devoted to the classification of irregular surfaces of general type with pg = q = 2 and non birational bicanonical map. The main result is that, if S is such a surface and if S is minimal with no pencil of curves of genus 2, then S is a double cover of a principally polarized abelian surface (A,Θ), with Θ irreducible. The double cover S → A is branched along a divisor B ∈ |...
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The moduli space M of surfaces of general type with pg = q = 1, K 2 = g = 3 (where g is the genus of the Albanese fibration) was constructed by Catanese and Ciliberto in [CaCi93]. In this paper we characterize the subvariety M 2 ⊂ M corresponding to surfaces containing a genus 2 pencil, and moreover we show that there exists a non-empty, dense subset M 0 ⊂ M which parametrizes isomorphism class...
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