Abstract
AbstractDenote by $${\mathbb {G}}(k,n)$$
G
(
k
,
n
)
the Grassmannian of linear subspaces of dimension k in $${\mathbb {P}}^n$$
P
n
. We show that if $$\varphi :{\mathbb {G}}(l,n) \rightarrow {\mathbb {G}}(k,n)$$
φ
:
G
(
l
,
n
)
→
G
(
k
,
n
)
is a nonconstant morphism and $$l \not =0,n-1$$
l
≠
0
,
n
-
1
, then $$l=k$$
l
=
k
or $$l=n-k-1$$
l
=
n
-
k
-
1
and $$\varphi $$
φ
is an isomorphism.
Funder
Università degli Studi di Trento
Publisher
Springer Science and Business Media LLC
Reference11 articles.
1. Brion, M.: Lectures on the geometry of flag varieties. In: Topics in Cohomological Studies of Algebraic Varieties, pp. 33–85. Trends Math., Birkhäuser, Basel (2005)
2. Eisenbud, D., Harris, J.: 3264 and all that—A Second Course in Algebraic Geometry. Cambridge University Press, Cambridge (2016)
3. Fulton, W.: Intersection Theory. Second Edition. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 2. Springer, Berlin (1998)
4. Fulton, W., MacPherson, R.D., Sottile, F., Sturmfels, B.: Intersection theory on spherical varieties. J. Algebra. Geom. 4(1), 181–193 (1995)
5. Haoqiang, H., Li, C., Liu, Z.: Effective good divisibility of rational homogeneous varieties. Math. Z. 305, 52 (2023)