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updated the dead link (the question has been bumped anyway by a new answer)
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Martin Sleziak
Martin Sleziak
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It seems a well-known fact that subvarieties of a variety of general type containing a general point are also of general type. This fact is an essential property used to prove some extension theorems of pluricanonical forms on algebraic varieties of general type, see for example the very nice survey on extension of pluricanonical forms

www-fourier.ujf-grenoble.fr/ECOLETE/2007/cours/pacienza.pdf.http://www.iecl.univ-lorraine.fr/~Gianluca.Pacienza/notes-grenoble.pdf (Internet Archive)

I want to know why this is true? Is there any thing more we can say about the relation between the canonical line bundle of a variety and that of subvaritiessubvarieties of codimension no less than 2.

It seems a well-known fact that subvarieties of a variety of general type containing a general point are also of general type. This fact is an essential property used to prove some extension theorems of pluricanonical forms on algebraic varieties of general type, see for example the very nice survey on extension of pluricanonical forms

www-fourier.ujf-grenoble.fr/ECOLETE/2007/cours/pacienza.pdf.

I want to know why this is true? Is there any thing more we can say about the relation between the canonical line bundle of a variety and that of subvarities of codimension no less than 2.

It seems a well-known fact that subvarieties of a variety of general type containing a general point are also of general type. This fact is an essential property used to prove some extension theorems of pluricanonical forms on algebraic varieties of general type, see for example the very nice survey on extension of pluricanonical forms

http://www.iecl.univ-lorraine.fr/~Gianluca.Pacienza/notes-grenoble.pdf (Internet Archive)

I want to know why this is true? Is there any thing more we can say about the relation between the canonical line bundle of a variety and that of subvarieties of codimension no less than 2.

added 45 characters in body; added 11 characters in body
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Fei YE
Fei YE
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It seems a well-known fact that subvarieties of a variety of general type containing a general point are also of general type. This fact is an essential propertiesproperty used to prove some extension theorems of pluricanonical forms on algebraic varietyvarieties of general type, see for example the very nice survey on extension of pluricanonical forms

www-fourier.ujf-grenoble.fr/ECOLETE/2007/cours/pacienza.pdf. I

I want to know why this is true? Is there any thing more we can say about the relation between the canonical line bundle of thea variety and that of subvarities of codimension no less than 2.

It seems a well-known fact that subvarieties of a variety of general type containing a general point are also of general type. This fact is essential properties used to prove some extension theorems of pluricanonical forms on algebraic variety of general type, see for example the very nice survey www-fourier.ujf-grenoble.fr/ECOLETE/2007/cours/pacienza.pdf. I want to know why this is true? Is there any thing more we can say about the relation between the canonical bundle of the variety and subvarities of codimension no less than 2.

It seems a well-known fact that subvarieties of a variety of general type containing a general point are also of general type. This fact is an essential property used to prove some extension theorems of pluricanonical forms on algebraic varieties of general type, see for example the very nice survey on extension of pluricanonical forms

www-fourier.ujf-grenoble.fr/ECOLETE/2007/cours/pacienza.pdf.

I want to know why this is true? Is there any thing more we can say about the relation between the canonical line bundle of a variety and that of subvarities of codimension no less than 2.

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Fei YE
Fei YE
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Why a subvariety of a variety of general type is of general type

It seems a well-known fact that subvarieties of a variety of general type containing a general point are also of general type. This fact is essential properties used to prove some extension theorems of pluricanonical forms on algebraic variety of general type, see for example the very nice survey www-fourier.ujf-grenoble.fr/ECOLETE/2007/cours/pacienza.pdf. I want to know why this is true? Is there any thing more we can say about the relation between the canonical bundle of the variety and subvarities of codimension no less than 2.