32
32

Sep 18, 2013
09/13

by
Baohua Fu

texts

######
eye 32

######
favorite 0

######
comment 0

We give two characterizations of hyperquadrics: one as non-degenerate smooth projective varieties swept out by large dimensional quadric subvarieties passing through a point; the other as $LQEL$-manifolds with large secant defects.

Source: http://arxiv.org/abs/0705.2927v1

53
53

Sep 22, 2013
09/13

by
Baohua Fu

texts

######
eye 53

######
favorite 0

######
comment 0

We prove the conjecture that two projective symplectic resolutions for a symplectic variety $W$ are related by Mukai's elementary transformations over $W$ in codimension 2 in the following cases: (i). nilpotent orbit closures in a classical simple complex Lie algebra; (ii). some quotient symplectic varieties.

Source: http://arxiv.org/abs/math/0409224v1

44
44

Sep 22, 2013
09/13

by
Baohua Fu

texts

######
eye 44

######
favorite 0

######
comment 0

A resolution $Z \to X$ of a Poisson variety $X$ is called {\em Poisson} if every Poisson structure on $X$ lifts to a Poisson structure on $Z$. For symplectic varieties, we prove that Poisson resolutions coincide with symplectic resolutions. It is shown that for a Poisson surface $S$, the natural resolution $S^{[n]} \to S^{(n)}$ is a Poisson resolution. Furthermore, if $Bs|-K_S| = \emptyset$, we prove that this is the unique projective Poisson resolution for $S^{(n)}$.

Source: http://arxiv.org/abs/math/0403408v2

65
65

Sep 23, 2013
09/13

by
Baohua Fu

texts

######
eye 65

######
favorite 0

######
comment 0

This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.

Source: http://arxiv.org/abs/math/0510346v1

50
50

Sep 18, 2013
09/13

by
Baohua Fu

texts

######
eye 50

######
favorite 0

######
comment 0

Let $\0$ be a nilpotent orbit in a semisimple complex Lie algebra $\g$. Denote by $G$ the simply connected Lie group with Lie algebra $\g$. For a $G$-homogeneous covering $M \to \0$, let $X$ be the normalization of $\bar{\0}$ in the function field of $M$. In this note, we study the existence of symplectic resolutions for such coverings $X$.

Source: http://arxiv.org/abs/math/0212024v1

46
46

Sep 21, 2013
09/13

by
Baohua Fu

texts

######
eye 46

######
favorite 0

######
comment 0

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.

Source: http://arxiv.org/abs/0905.4114v1

55
55

Sep 18, 2013
09/13

by
Baohua Fu

texts

######
eye 55

######
favorite 0

######
comment 0

In a recent preprint, Y. Namikawa proposed a conjecture on Q-factorial terminalizations and their birational geometry of nilpotent orbits. He proved his conjecture for classical simple Lie algebras. In this note, we prove his conjecture for exceptional simple Lie algebras. For the birational geometry, contrary to the classical case, two new types of Mukai flops appear.

Source: http://arxiv.org/abs/0809.5109v2

37
37

Sep 19, 2013
09/13

by
Baohua Fu

texts

######
eye 37

######
favorite 0

######
comment 0

Let $S$ be a smooth complex connected analytic surface which admits a holomorphic symplectic structure. Let $S^{(n)}$ be its $n$th symmetric product. We prove that every projective symplectic resolution of $S^{(n)}$ is isomorphic to the Douady-Barlet resolution $S^{[n]} \to S^{(n)}$.

Source: http://arxiv.org/abs/math/0304066v1

38
38

Sep 23, 2013
09/13

by
Baohua Fu

texts

######
eye 38

######
favorite 0

######
comment 0

We prove that two projective symplectic resolutions of $\cit^{2n}/G$ are connected by Mukai flops in codimension 2 for a finite sub-group $G < \Sp(2n)$. It is also shown that two projective symplectic resolutions of $\cit^4/G$ are deformation equivalent.

Source: http://arxiv.org/abs/math/0510347v1

39
39

Sep 18, 2013
09/13

by
Baohua Fu

texts

######
eye 39

######
favorite 0

######
comment 0

We prove that two Springer maps over a nilpotent orbit closure with the same degree are connected by stratified Mukai flops and the latter is obtained by extremal contractions of a natural resolution of the nilpotent orbit closure.

Source: http://arxiv.org/abs/math/0605431v1

100
100

Sep 21, 2013
09/13

by
Baohua Fu

texts

######
eye 100

######
favorite 0

######
comment 0

The projectivised nilpotent orbit closure P(\bar{O}) carries a natural contact structure on its smooth part. A resolution X \to P(\bar{O}) is called contact if the contact structure on P(O) extends to a contact structure on X. It turns out that contact resolutions, crepant resolutions and minimal models of P(\bar{O}) are all the same. In this note, we determine when the projectivised nilpotent orbit closure admits a contact resolution, and in the case of existence, we study the birational...

Source: http://arxiv.org/abs/math/0602088v2

35
35

Sep 19, 2013
09/13

by
Baohua Fu

texts

######
eye 35

######
favorite 0

######
comment 0

We give some necessary conditions for the existence of a symplectic resolution for quotient singularities. The McKay correspondence is also worked out for these resolutions.

Source: http://arxiv.org/abs/math/0206288v2

40
40

Sep 21, 2013
09/13

by
Baohua Fu

texts

######
eye 40

######
favorite 0

######
comment 0

In this note, firstly we give an easy proof of the factorization of symmetric matrices (see [Mos] math-ph/0203023), then we use it to prove the well-known fact that the automorphism group of a non-degenerate symmetric bilinear form acts transitively on the locus of isotropic subspaces \Sigma_k.

Source: http://arxiv.org/abs/math/0203154v1

47
47

Sep 18, 2013
09/13

by
Baohua Fu

texts

######
eye 47

######
favorite 0

######
comment 0

We prove that for any two projective symplectic resolutions $Z_1$ and $Z_2$ for a nilpotent orbit closure in a complex simple Lie algebra of classical type, then $Z_1$ is deformation equivalen to $Z_2$.

Source: http://arxiv.org/abs/math/0306090v2

47
47

Sep 22, 2013
09/13

by
Baohua Fu

texts

######
eye 47

######
favorite 0

######
comment 0

We prove that any symplectic resolution of the closure of a nilpotent orbit in a semi-simple complex Lie algebra is isomorphic to the collapsing of the cotangent bundle of a projective homogenous variety. Then we give a complete characterization of those nilpotent orbits whose closure admit a symplectic resolution.

Source: http://arxiv.org/abs/math/0205048v2

56
56

Sep 18, 2013
09/13

by
Baohua Fu

texts

######
eye 56

######
favorite 0

######
comment 0

We recover a 4-dimensional wreath product X as a transversal slice to a nilpotent orbit in sp_6. By using deformations of Springer resolutions, we construct a symplectic deformation of symplectic resolutions of X.

Source: http://arxiv.org/abs/math/0611472v1

4
4.0

Jun 27, 2018
06/18

by
Michel Brion; Baohua Fu

texts

######
eye 4

######
favorite 0

######
comment 0

Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general point. As an application, we show that X has the target rigidity property when G is not of type A_1 or C.

Topics: Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1503.02275

43
43

Sep 18, 2013
09/13

by
Baohua Fu; Yoshinori Namikawa

texts

######
eye 43

######
favorite 0

######
comment 0

We prove the uniqueness of crepant resolutions for some quotient singularities and for some nilpotent orbits. The finiteness of non-isomorphic symplectic resolutions for 4-dimenensional symplectic singularities is proved. We also give an example of symplectic singularity which admits two non-equivalent symplectic resolutions.

Source: http://arxiv.org/abs/math/0306091v2

49
49

Sep 21, 2013
09/13

by
Baohua Fu; Fabien Herbaut

texts

######
eye 49

######
favorite 0

######
comment 0

We consider the Chow ring with rational coefficients of the Jacobian of a curve. Assume D is a divisor in a base point free g^r_d of the curve such that the canonical divisor K is a multiple of the divisor D. We find relations between tautological cycles. We give applications for curves having a degree d covering of P^1 whose ramification points are all of order d, and then for hyperelliptic curves.

Source: http://arxiv.org/abs/0706.2814v1

34
34

Sep 21, 2013
09/13

by
Baohua Fu; Jun-Muk Hwang

texts

######
eye 34

######
favorite 0

######
comment 0

Let X be an $n$-dimensional Fano manifold of Picard number 1. We study how many different ways X can compactify the complex vector group C^n equivariantly. Hassett and Tschinkel showed that when X = P^n with n \geq 2, there are many distinct ways that X can be realized as equivariant compactifications of C^n. Our result says that projective space is an exception: among Fano manifolds of Picard number 1 with smooth VMRT, projective space is the only one compactifying C^n equivariantly in more...

Source: http://arxiv.org/abs/1301.5486v1

38
38

Sep 23, 2013
09/13

by
Baohua Fu; Chin-Lung Wang

texts

######
eye 38

######
favorite 0

######
comment 0

For stratified Mukai flops of type $A_{n,k}, D_{2k+1}$ and $E_{6,I}$, it is shown the fiber product induces isomorphisms on Chow motives. In contrast to (standard) Mukai flops, the cup product is generally not preserved. For $A_{n, 2}$, $D_5$ and $E_{6, I}$ flops, quantum corrections are found through degeneration/deformation to ordinary flops.

Source: http://arxiv.org/abs/0801.3551v2

64
64

Sep 21, 2013
09/13

by
Baohua Fu; Jun-Muk Hwang

texts

######
eye 64

######
favorite 0

######
comment 0

The prolongation g^{(k)} of a linear Lie algebra g \subset gl(V) plays an important role in the study of symmetries of G-structures. Cartan and Kobayashi-Nagano have given a complete classification of irreducible linear Lie algebras g \subset gl(V) with non-zero prolongations. If g is the Lie algebra aut(\hat{S}) of infinitesimal linear automorphisms of a projective variety S \subset \BP V, its prolongation g^{(k)} is related to the symmetries of cone structures, an important example of which...

Source: http://arxiv.org/abs/1011.4751v1

4
4.0

Jun 26, 2018
06/18

by
Baohua Fu; Jun-Muk Hwang

texts

######
eye 4

######
favorite 0

######
comment 0

A birational transformation f: P^n --> Z, where Z is a nonsingular variety of Picard number 1, is called a special birational transformation of type (a, b) if f is given by a linear system of degree a, its inverse is given by a linear system of degree b and the base locus S \subset P^n of f is irreducible and nonsingular. In this paper, we classify special birational transformations of type (2,1). In addition to previous works Alzati-Sierra and Russo on this topic, our proof employs natural...

Topics: Mathematics, Algebraic Geometry

Source: http://arxiv.org/abs/1501.04410

37
37

Sep 17, 2013
09/13

by
Baohua Fu; Jun-Muk Hwang

texts

######
eye 37

######
favorite 0

######
comment 0

We shall show that the variety of minimal rational tangents on a complete toric manifold X is linear and minimal components in RatCurves^n(X) corresponds bijectively to some special primitive collections in the fan defining X.

Source: http://arxiv.org/abs/0912.1638v1

40
40

Sep 18, 2013
09/13

by
Pierre-Emmanuel Chaput; Baohua Fu

texts

######
eye 40

######
favorite 0

######
comment 0

We construct a resolution of stratified Mukai flops of type A, D, E_{6, I} by successively blowing up smooth subvarieties. In the case of E_{6, I}, we construct a natural functor which induces an isomorphism between the Chow groups.

Source: http://arxiv.org/abs/math/0611470v1

39
39

Sep 20, 2013
09/13

by
Baohua Fu; De-Qi Zhang

texts

######
eye 39

######
favorite 0

######
comment 0

We show that a compact Kaehler manifold X is a complex torus if both the continuous part and discrete part of some automorphism group G of X are infinite groups, unless X is bimeromorphic to a non-trivial G-equivariant fibration. Some applications to dynamics are given.

Source: http://arxiv.org/abs/1205.0607v2

9
9.0

Jun 26, 2018
06/18

by
Baohua Fu; Daniel Juteau; Paul Levy; Eric Sommers

texts

######
eye 9

######
favorite 0

######
comment 0

According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity of the nilpotent cone, the closure of the minimal nilpotent orbit is also an isolated symplectic singularity, called a minimal singularity. For classical Lie algebras, Kraft and Procesi showed that these two types of singularities suffice to describe all...

Topics: Mathematics, Algebraic Geometry, Representation Theory

Source: http://arxiv.org/abs/1502.05770