Results 11 to 20 of about 619 (63)
Nonsolidity of uniruled varieties
Forum of Mathematics, Sigma, 2023 We give conditions for a uniruled variety of dimension at least 2 to be nonsolid. This study provides further evidence to a conjecture by Abban and Okada on the solidity of Fano 3-folds.
Livia Campo, Tiago Duarte Guerreiro
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Decompositions of moduli spaces of vector bundles and graph potentials
Forum of Mathematics, Sigma, 2023 We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for and furthermore propose
Pieter Belmans +2 more
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Gushel--Mukai varieties: intermediate Jacobians [PDF]
Épijournal de Géométrie Algébrique, 2020 We describe intermediate Jacobians of Gushel-Mukai varieties $X$ of dimensions 3 or 5: if $A$ is the Lagrangian space associated with $X$, we prove that the intermediate Jacobian of $X$ is isomorphic to the Albanese variety of the canonical double ...
Olivier Debarre, Alexander Kuznetsov
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K-stability of Fano varieties via admissible flags
Forum of Mathematics, Pi, 2022 We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces ...
Hamid Abban, Ziquan Zhuang
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FANO HYPERSURFACES WITH ARBITRARILY LARGE DEGREES OF IRRATIONALITY
Forum of Mathematics, Sigma, 2020 We show that complex Fano hypersurfaces can have arbitrarily large degrees of irrationality. More precisely, if we fix a Fano index $e$, then the degree of irrationality of a very general complex Fano hypersurface of index $e$ and dimension n is bounded ...
NATHAN CHEN, DAVID STAPLETON
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The number of vertices of a Fano polytope [PDF]
, 2004 Let X be a complex, Gorenstein, Q-factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of X in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number
Casagrande, C.
core +6 more sources
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
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The classification of smooth toric weakened Fano 3-folds [PDF]
, 2002 We completely classify toric weakened Fano 3-folds, that is, smooth toric weak Fano 3-folds which are not Fano but are deformed to smooth Fano 3-folds.
Sato, Hiroshi
core +1 more source
The Ricci iteration and its applications [PDF]
, 2007 In this Note we introduce and study dynamical systems related to the Ricci operator on the space of Kahler metrics as discretizations of certain geometric flows.
Rubinstein, Yanir A.
core +3 more sources
Jumping deformations of complete toric varieties
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 49, Page 3101-3113, 2003., 2003 We construct one‐parameter complex analytic families whose special fibers are complete toric varieties. Under appropriate assumptions, the general fibers of these families also become toric varieties, and the corresponding fans are explicitly described by the data of the fans associated to the special fibers.
Hiroshi Sato
wiley +1 more source