Mixing
Hodge theory (after Deligne)
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In an interview with Deligne on the Simons Foundation website, I heard Robert MacPherson say that at the time Deligne's papers on Hodge theory were being published, the results seemed absolutely miraculous to specialists in Algebraic Geometry.
Can anyone explain why this is ?
ag.algebraic-geometry cohomology schemes hodge-theory zeta-functions
asked 2 hours ago
THC
853613
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up vote
7
down vote
favorite
In an interview with Deligne on the Simons Foundation website, I heard Robert MacPherson say that at the time Deligne's papers on Hodge theory were being published, the results seemed absolutely miraculous to specialists in Algebraic Geometry.
Can anyone explain why this is ?
ag.algebraic-geometry cohomology schemes hodge-theory zeta-functions
asked 2 hours ago
THC
853613
A while back I found this video of the lecture "Hodge Theory -- From Abel to Deligne" by Phillip Griffiths" youtube.com/watch?v=hPyDz5R5YaY rather enlightening.
– j.c.
10 mins ago
add a comment |Â
up vote
7
down vote
favorite
up vote
7
down vote
favorite
In an interview with Deligne on the Simons Foundation website, I heard Robert MacPherson say that at the time Deligne's papers on Hodge theory were being published, the results seemed absolutely miraculous to specialists in Algebraic Geometry.
Can anyone explain why this is ?
ag.algebraic-geometry cohomology schemes hodge-theory zeta-functions
asked 2 hours ago
THC
853613
In an interview with Deligne on the Simons Foundation website, I heard Robert MacPherson say that at the time Deligne's papers on Hodge theory were being published, the results seemed absolutely miraculous to specialists in Algebraic Geometry.
Can anyone explain why this is ?
ag.algebraic-geometry cohomology schemes hodge-theory zeta-functions
ag.algebraic-geometry cohomology schemes hodge-theory zeta-functions
asked 2 hours ago
THC
853613
asked 2 hours ago
THC
853613
asked 2 hours ago
THC
853613
asked 2 hours ago
THC
853613
asked 2 hours ago
THC
853613
853613
A while back I found this video of the lecture "Hodge Theory -- From Abel to Deligne" by Phillip Griffiths" youtube.com/watch?v=hPyDz5R5YaY rather enlightening.
– j.c.
10 mins ago
add a comment |Â
A while back I found this video of the lecture "Hodge Theory -- From Abel to Deligne" by Phillip Griffiths" youtube.com/watch?v=hPyDz5R5YaY rather enlightening.
– j.c.
10 mins ago
A while back I found this video of the lecture "Hodge Theory -- From Abel to Deligne" by Phillip Griffiths" youtube.com/watch?v=hPyDz5R5YaY rather enlightening.
– j.c.
10 mins ago
A while back I found this video of the lecture "Hodge Theory -- From Abel to Deligne" by Phillip Griffiths" youtube.com/watch?v=hPyDz5R5YaY rather enlightening.
– j.c.
10 mins ago
add a comment |Â
1 Answer
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The laudatio for the Wolf prize explains it like this:
Central to modern algebraic geometry is the theory of moduli, i.e.,
variation of algebraic or analytic structure. This theory was
traditionally mysterious and problematic. In critical special cases,
i.e., curves, it made sense, i.e., the set of curves of genus greater
than one had a natural algebraic structure. In dimensions greater than
one, there was some sort of structure locally, but globally everything
remained mysterious. [...] Building on Mumford’s and Griffiths’ work,
Pierre Deligne demonstrated how to extend the variation of Hodge
theory to singular varieties. This advance, called mixed Hodge theory,
allowed explicit calculation on the singular compactification of
moduli spaces that came up in Mumford’s geometric invariant theory.
answered 29 mins ago
Carlo Beenakker
69.6k8155261
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
The laudatio for the Wolf prize explains it like this:
Central to modern algebraic geometry is the theory of moduli, i.e.,
variation of algebraic or analytic structure. This theory was
traditionally mysterious and problematic. In critical special cases,
i.e., curves, it made sense, i.e., the set of curves of genus greater
than one had a natural algebraic structure. In dimensions greater than
one, there was some sort of structure locally, but globally everything
remained mysterious. [...] Building on Mumford’s and Griffiths’ work,
Pierre Deligne demonstrated how to extend the variation of Hodge
theory to singular varieties. This advance, called mixed Hodge theory,
allowed explicit calculation on the singular compactification of
moduli spaces that came up in Mumford’s geometric invariant theory.
answered 29 mins ago
Carlo Beenakker
69.6k8155261
add a comment |Â
up vote
4
down vote
The laudatio for the Wolf prize explains it like this:
Central to modern algebraic geometry is the theory of moduli, i.e.,
variation of algebraic or analytic structure. This theory was
traditionally mysterious and problematic. In critical special cases,
i.e., curves, it made sense, i.e., the set of curves of genus greater
than one had a natural algebraic structure. In dimensions greater than
one, there was some sort of structure locally, but globally everything
remained mysterious. [...] Building on Mumford’s and Griffiths’ work,
Pierre Deligne demonstrated how to extend the variation of Hodge
theory to singular varieties. This advance, called mixed Hodge theory,
allowed explicit calculation on the singular compactification of
moduli spaces that came up in Mumford’s geometric invariant theory.
answered 29 mins ago
Carlo Beenakker
69.6k8155261
add a comment |Â
up vote
4
down vote
up vote
4
down vote
The laudatio for the Wolf prize explains it like this:
Central to modern algebraic geometry is the theory of moduli, i.e.,
variation of algebraic or analytic structure. This theory was
traditionally mysterious and problematic. In critical special cases,
i.e., curves, it made sense, i.e., the set of curves of genus greater
than one had a natural algebraic structure. In dimensions greater than
one, there was some sort of structure locally, but globally everything
remained mysterious. [...] Building on Mumford’s and Griffiths’ work,
Pierre Deligne demonstrated how to extend the variation of Hodge
theory to singular varieties. This advance, called mixed Hodge theory,
allowed explicit calculation on the singular compactification of
moduli spaces that came up in Mumford’s geometric invariant theory.
answered 29 mins ago
Carlo Beenakker
69.6k8155261
The laudatio for the Wolf prize explains it like this:
Central to modern algebraic geometry is the theory of moduli, i.e.,
variation of algebraic or analytic structure. This theory was
traditionally mysterious and problematic. In critical special cases,
i.e., curves, it made sense, i.e., the set of curves of genus greater
than one had a natural algebraic structure. In dimensions greater than
one, there was some sort of structure locally, but globally everything
remained mysterious. [...] Building on Mumford’s and Griffiths’ work,
Pierre Deligne demonstrated how to extend the variation of Hodge
theory to singular varieties. This advance, called mixed Hodge theory,
allowed explicit calculation on the singular compactification of
moduli spaces that came up in Mumford’s geometric invariant theory.
answered 29 mins ago
Carlo Beenakker
69.6k8155261
answered 29 mins ago
Carlo Beenakker
69.6k8155261
answered 29 mins ago
Carlo Beenakker
69.6k8155261
answered 29 mins ago
Carlo Beenakker
69.6k8155261
69.6k8155261
add a comment |Â
add a comment |Â
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A while back I found this video of the lecture "Hodge Theory -- From Abel to Deligne" by Phillip Griffiths" youtube.com/watch?v=hPyDz5R5YaY rather enlightening.
– j.c.
10 mins ago