Results 11 to 20 of about 58 (58)

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, Sergey Galkin, Swarnava Mukhopadhyay   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Pluricomplex Green's functions and Fano manifolds [PDF]

Épijournal de Géométrie Algébrique, 2019
We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere ...
Nicholas McCleerey, Valentino Tosatti
doaj   +1 more source

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

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

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

K-moduli of pure states of four qubits [PDF]

MSC classes: 14J45, 14J30, 32Q20.We find all K-polystable limits of divisors in (P^1)^4 of degree (1,1,1,1) and explicitly describe the associated irreducible component of the K-moduli ...
Kaloghiros, A-S, Cheltsov, I, Fedorchuk, M, Fujita, K   +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