Results 21 to 30 of about 599 (45)

Conic bundles that are not birational to numerical Calabi--Yau pairs [PDF]

Épijournal de Géométrie Algébrique, 2017
Let $X$ be a general conic bundle over the projective plane with branch curve of degree at least 19. We prove that there is no normal projective variety $Y$ that is birational to $X$ and such that some multiple of its anticanonical divisor is effective ...
János Kollár
doaj   +1 more source

Characterization theorems for the projective space and vector bundle adjunction [PDF]

, 2003
We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction.
Andreatta, Marco
core   +2 more sources

ON TORUS ACTIONS OF HIGHER COMPLEXITY

Forum of Mathematics, Sigma, 2019
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring theory. Our approach
JÜRGEN HAUSEN, CHRISTOFF HISCHE, MILENA WROBEL   +2 more
doaj   +1 more source

Manifolds covered by lines and the Hartshorne Conjecture for quadratic manifolds

, 2012
Small codimensional embedded manifolds defined byequations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension.
Ionescu, Paltin, Russo, Francesco
core   +2 more sources

Slopes of smooth curves on Fano manifolds

, 2011
Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds of dimension $
Hwang, Jun-Muk, Kim, Hosung, Lee, Yongnam, Park, Jihun   +3 more
core   +1 more source

Global F-regularity for weak del Pezzo surfaces

Forum of Mathematics, Sigma
Let k be an algebraically closed field of characteristic $p>0$ . Let X be a normal projective surface over k with canonical singularities whose anticanonical divisor is nef and big.
Tatsuro Kawakami, Hiromu Tanaka
doaj   +1 more source

On $G$-birational rigidity of del Pezzo surfaces [PDF]

Épijournal de Géométrie Algébrique
Let $G$ be a finite group and $H\subseteq G$ be its subgroup. We prove that if a smooth del Pezzo surface over an algebraically closed field is $H$-birationally rigid then it is also $G$-birationally rigid, answering a geometric version of Koll\'{a}r's ...
Egor Yasinsky
doaj   +1 more source

An invariant for embedded Fano manifolds covered by linear spaces

, 2017
For an embedded Fano manifold $X$, we introduce a new invariant $S_X$ related to the dimension of covering linear spaces.
Suzuki, Taku
core   +1 more source

Kawamata-Miyaoka-type inequality for $\mathbb Q$-Fano varieties with canonical singularities II: Terminal $\mathbb Q$-Fano threefolds [PDF]

Épijournal de Géométrie Algébrique
We prove an optimal Kawamata-Miyaoka-type inequality for terminal $\mathbb Q$-Fano threefolds with Fano index at least $3$. As an application, any terminal $\mathbb Q$-Fano threefold $X$ satisfies the following Kawamata-Miyaoka-type inequality \[ c_1(X ...
Haidong Liu, Jie Liu
doaj   +1 more source

Unipotent Group Actions on Del Pezzo Cones

, 2013
In a previous paper we established that for any del Pezzo surface Y of degree at least 4, the affine cone X over Y embedded via a pluri-anticanonical linear system admits an effective Ga-action. In particular, the group Aut(X) is infinite dimensional. In
Kishimoto, Takashi, Prokhorov, Yuri, Zaidenberg, Mikhail   +2 more
core   +3 more sources