Some (big) irreducible components of the moduli space of minimal surfaces of general type with $p_g= q = 1$ and $K^2 = 4$ | Zendy

Roberto Pignatelli | Zendy

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Some (big) irreducible components of the moduli space of minimal surfaces of general type with $p_g= q = 1$ and $K^2 = 4$

Author(s) -

Roberto Pignatelli

Publication year - 2009

Publication title -

rendiconti lincei matematica e applicazioni

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.824

H-Index - 28

eISSN - 1720-0768

pISSN - 1120-6330

DOI - 10.4171/rlm/544

Subject(s) - mathematics , moduli space , type (biology) , space (punctuation) , moduli , irreducible component , pure mathematics , combinatorics , mathematical analysis , physics , differential algebraic equation , ecology , ordinary differential equation , linguistics , philosophy , quantum mechanics , biology , differential equation

In this paper we study the minimal surfaces of general type with $p_g=q=1$ and $K^2=4$ whose Albanese general fibre has genus 2, classifying those such that the direct image (under the Albanese morphism) of the bicanonical sheaf is sum of line bundles. We find 8 unirational families, all of dimension strictly bigger than the expected one. These families are pairwise disjoint irreducible components of the moduli space of minimal surfaces of general type.

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