Termination of (many) 4-dimensional log flips

We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(K+D) is numerically equivalent to an effective divisor, terminates. This implies termination of flips that begin with a log Fano pair and termination of flips in a relative birational setting. We also prove termination of directed flips with big K+D. As a consequence, we prove existence of minimal models of 4-dimensional dlt pairs of general type, existence of 5-dimensional log flips, and rationality of Kodaira energy in dimension 4.Comment: 13 pages; a minor change in the proof of Thm.4.

Thermal Conductivity in the Bose-Einstein Condensed State of Triplons in the Bond-Alternating Spin-Chain System Pb2V3O9

In order to clarify the origin of the enhancement of the thermal conductivity in the Bose-Einstein Condensed (BEC) state of field-induced triplons, we have measured the thermal conductivity along the [101] direction parallel to spin-chains, $kappa_{\|[101]}$, and perpendicular to spin-chains, $kappa_{\perp[101]}$, of the S=1/2 bond-alternating spin-chain system Pb2V3O9 in magnetic fields up to 14 T. With increasing field at 3 K, it has been found that both $kappa_{\|[101]}$ and $kappa_{\perp[101]}$ are suppressed in the gapped normal state in low fields. In the BEC state of field-induced triplons in high fields, on the other hand, $kappa_{\|[101]}$ is enhanced with increasing field, while $kappa_{\perp[101]}$ is suppressed. That is, the thermal conductivity along the direction, where the magnetic interaction is strong, is markedly enhanced in the BEC state. Accordingly, our results suggest that the enhancement of $kappa_{\|[101]}$ in the BEC state is caused by the enhancement of the thermal conductivity due to triplons on the basis of the two-fluid model, as in the case of the superfluid state of liquid 4He.Comment: 5 pages, 3 figure

Characterization of the 4-canonical birationality of algebraic threefolds

In this article we present a 3-dimensional analogue of a well-known theorem of E. Bombieri (in 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let $X$ be a projective minimal 3-fold of general type with $\mathbb{Q}$-factorial terminal singularities and the geometric genus $p_g(X)\ge 5$. We show that the 4-canonical map $\phi_4$ is {\it not} birational onto its image if and only if $X$ is birationally fibred by a family $\mathscr{C}$ of irreducible curves of geometric genus 2 with $K_X\cdot C_0=1$ where $C_0$ is a general irreducible member in $\mathscr{C}$.Comment: 25 pages, to appear in Mathematische Zeitschrif

Anti-Pluricanonical Systems On Q-Fano Threefolds

We investigate birationality of the anti-pluricanonical map $\phi_{-m}$, the rational map defined by the anti-pluricanonical system $|-mK|$, on $\mathbb{Q}$-Fano threefolds.Comment: 18 page

A high fibered power of a family of varieties of general type dominates a variety of general type

We prove the following theorem: Fibered Power Theorem: Let X\rar B be a smooth family of positive dimensional varieties of general type, with $B$ irreducible. Then there exists an integer $n>0$, a positive dimensional variety of general type $W_n$, and a dominant rational map X^n_B \das W_n.Comment: Latex2e (in latex 2.09 compatibility mode). To get a fun-free version change the `FUN' variable to `n' on the second line (option dedicated to my friend Yuri Tschinkel). Postscript file with color illustration available on http://math.bu.edu/INDIVIDUAL/abrmovic/fibered.p

Holomorphic symmetric differentials and a birational characterization of Abelian Varieties

A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to an abelian variety if and only if it has Kodaira dimension 0 and some symmetric power of its cotangent sheaf is generically generated by its global sections.Comment: UPDATED: more details added on main proo

Three embeddings of the Klein simple group into the Cremona group of rank three

We study the action of the Klein simple group G consisting of 168 elements on two rational threefolds: the three-dimensional projective space and a smooth Fano threefold X of anticanonical degree 22 and index 1. We show that the Cremona group of rank three has at least three non-conjugate subgroups isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein metric, and we construct a smooth polarized K3 surface of degree 22 with an action of the group G.Comment: 43 page

Logarithmic Moduli Spaces for Surfaces of Class VII

In this paper we describe logarithmic moduli spaces of pairs (S,D) consisting of minimal surfaces S of class VII with positive second Betti number b_2 together with reduced divisors D of b_2 rational curves. The special case of Enoki surfaces has already been considered by Dloussky and Kohler. We use normal forms for the action of the fundamental group of the complement of D and for the associated holomorphic contraction germ from (C^2,0) to (C^2,0).Comment: Minor correction of the dimension of the moduli spac

Enhancement of electronic anomalies in iron-substituted La_2-x_Sr_x_Cu_1-y_Fe_y_O_4_ around x=0.22

We have measured the temperature dependences of Rho and Chi for Fe-substituted La_2-x_Sr_x_Cu_1-y_Fe_y_O_4_ in the overdoped regime, in order to investigate Fe-substitution effects on electronic properties around x=0.22. From the Rho measurements, it has been found around x=0.22 that the values of Rho are large at room temperature and that Rho exhibits a pronounced upturn at low temperatures. Moreover, from the Rho and Chi measurements, it has been found that T_c_ is anomalously depressed around x=0.22. These results indicate that the electronic anomalies around x=0.22 are enhanced by Fe substitution, which might be related to the development of stripe correlations by Fe substitution.Comment: 7 pages, 3 figure

Fundamental groups of open K3 surfaces, Enriques surfaces and Fano 3-folds

We investigate when the fundamental group of the smooth part of a K3 surface or Enriques surface with Du Val singularities, is finite. As a corollary we give an effective upper bound for the order of the fundamental group of the smooth part of a certain Fano 3-fold. This result supports Conjecture A below, while Conjecture A (or alternatively the rational connectedness conjecture in [KoMiMo] which is still open when the dimension is at least 4) would imply that every log terminal Fano variety has a finite fundamental group (now a Theorem of S. Takayama).Comment: Journal of Pure and Applied Algebra, to appear; 24 page