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Title: On the geometry of a smooth model of a fibre product of families of K3 surfaces

Abstract

The Hodge conjecture on algebraic cycles is proved for a smooth projective model X of a fibre product X{sub 1}×{sub C}X{sub 2} of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) X{sub k}→C (k=1,2) over a smooth projective curve C under the assumption that, for generic geometric fibres X{sub 1s} and X{sub 2s}, the ring End{sub Hg(X{sub 1{sub s)}}}NS{sub Q}(X{sub 1s}){sup ⊥} is an imaginary quadratic field, rankNS(X{sub 1s})≠18, and End{sub Hg(X{sub 2{sub s)}}}NS{sub Q}(X{sub 2s}){sup ⊥} is a totally real field or else rankNS(X{sub 1s})

Authors:
 [1]
  1. A.G. and N.G.Stoletov Vladimir State University, Vladimir (Russian Federation)
Publication Date:
OSTI Identifier:
22365738
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; DIAGRAMS; FIBERS; GEOMETRY; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; SURFACES

Citation Formats

Nikol'skaya, O V. On the geometry of a smooth model of a fibre product of families of K3 surfaces. United States: N. p., 2014. Web. doi:10.1070/SM2014V205N02ABEH004374.
Nikol'skaya, O V. On the geometry of a smooth model of a fibre product of families of K3 surfaces. United States. doi:10.1070/SM2014V205N02ABEH004374.
Nikol'skaya, O V. Fri . "On the geometry of a smooth model of a fibre product of families of K3 surfaces". United States. doi:10.1070/SM2014V205N02ABEH004374.
@article{osti_22365738,
title = {On the geometry of a smooth model of a fibre product of families of K3 surfaces},
author = {Nikol'skaya, O V},
abstractNote = {The Hodge conjecture on algebraic cycles is proved for a smooth projective model X of a fibre product X{sub 1}×{sub C}X{sub 2} of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) X{sub k}→C (k=1,2) over a smooth projective curve C under the assumption that, for generic geometric fibres X{sub 1s} and X{sub 2s}, the ring End{sub Hg(X{sub 1{sub s)}}}NS{sub Q}(X{sub 1s}){sup ⊥} is an imaginary quadratic field, rankNS(X{sub 1s})≠18, and End{sub Hg(X{sub 2{sub s)}}}NS{sub Q}(X{sub 2s}){sup ⊥} is a totally real field or else rankNS(X{sub 1s})},
doi = {10.1070/SM2014V205N02ABEH004374},
journal = {Sbornik. Mathematics},
number = 2,
volume = 205,
place = {United States},
year = {Fri Feb 28 00:00:00 EST 2014},
month = {Fri Feb 28 00:00:00 EST 2014}
}
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