By Fabrizio Catanese, Hélène Esnault, Alan Huckleberry, Klaus Hulek, Thomas Peternell

ISBN-10: 3540354794

ISBN-13: 9783540354796

This number of surveys current an summary of contemporary advancements in advanced Geometry. issues variety from curve and floor conception via targeted forms in better dimensions, moduli conception, Kähler geometry, and team activities to Hodge idea and attribute p-geometry.

Written via proven specialists this ebook may be a needs to for mathematicians operating in complicated Geometry

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Surfaces with K 2 = pg = 1 and their period mapping. In: Algebraic geometry (Proc. Summer Meeting, Univ.

Remark 21. 1) In [Cat02] the second author shows that Manetti’s examples are indeed symplectomorphic. 2) A possible way of showing that the answer to the question above is yes (and therefore exhibiting symplectomorphic simply connected surfaces which are not def-equivalent) goes through the analysis of the braid monodromy of the branch curve of the “perturbed” (corresponding to the Lefschetz ﬁbration) quadruple covering, and one would like to show that the involution ι on P1 , ι(y) = −y can be written as the product of braids which show up in the factorization.

Therefore, if one gives at least three surfaces, which are pairwise diﬀeomorphic, one ﬁnds at least two surfaces with the property that there exists a diﬀeomorphism between them sending the canonical class of one to the canonical class of the other. Theorem 32. ([CW04]) For each natural number h there are simply connected surfaces S1 , . . , Sh which are pairwise diﬀeomorphic, but are such that two of them are never def-equivalent. Complex Surfaces of General Type: Some Recent Progress 45 The above surfaces S1 , .

### Global Aspects of Complex Geometry by Fabrizio Catanese, Hélène Esnault, Alan Huckleberry, Klaus Hulek, Thomas Peternell

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