Abstract
AbstractWe study varieties $$X \subseteq {\mathbb {P}}^N$$
X
⊆
P
N
of dimension n such that $$T_X(k)$$
T
X
(
k
)
is an Ulrich vector bundle for some $$k \in {\mathbb {Z}}$$
k
∈
Z
. First we give a sharp bound for k in the case of curves. Then we show that $$k \le n+1$$
k
≤
n
+
1
if $$2 \le n \le 12$$
2
≤
n
≤
12
. We classify the pairs $$(X,{\mathcal {O}}_X(1))$$
(
X
,
O
X
(
1
)
)
for $$k=1$$
k
=
1
and we show that, for $$n \ge 4$$
n
≥
4
, the case$$k=2$$
k
=
2
does not occur.
Funder
Università degli Studi Roma Tre
Publisher
Springer Science and Business Media LLC
Reference34 articles.
1. Ambro, F.: Ladders on Fano varieties. Algebraic geometry, 9. J. Math. Sci. (N.Y.) 94(1), 1126–1135 (1999)
2. Beauville, A.: An introduction to Ulrich bundles. Eur. J. Math. 4(1), 26–36 (2018)
3. Beauville, A.: Complex Algebraic Surfaces. London Mathematical Society Lecture Note Series, 68. Cambridge University Press, Cambridge, iv+132 pp (1983)
4. Bauer, I., Catanese, F.: On rigid compact complex surfaces and manifolds. Adv. Math. 333, 620–669 (2018)
5. Bogomolov, F., McQuillan, M.: Rational curves on foliated varieties. Foliation theory in algebraic geometry. In: Simons Symp., pp. 21–51. Springer, Cham (2016)