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Toric degenerations and Gromov width of smooth projective varieties | | Kiumars Kaveh
; | | Date: |
3 Aug 2015 | | Abstract: | Let $X subset mathbb{C}mathbb{P}^{r-1}$ be an $n$-dimensional smooth
complex projective variety equipped with a Kahler structure given by a
Fubini-Study Kahler form on $mathbb{C}mathbb{P}^{r-1}$. We show that $X$ has
an open subset $U$ (in the usual classical topology) which is symplectomorphic
to the torus $(mathbb{C}^*)^n$ equipped with an integral toric Kahler form
induced by a monomial embedding in $mathbb{C}mathbb{P}^{r-1}$. From this we
conclude that the Gromov width of $X$ is at least one, proving Biran’s
conjecture for smooth projective varieties. Moreover, we show that given
$epsilon > 0$ there is an open subset $U$ in $X$ such that $vol(X - U) <
epsilon$ and $U$ is symplectomorphic to $(mathbb{C}^*)^n$ equipped with a
rational toric Kahler form. | | Source: | arXiv, 1508.0316 | | Services: | Forum | Review | PDF | Favorites | |
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