In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical variet...In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs（X, Δ） when X is a projective horospherical variety.展开更多
We show the validity of the relative dlt MMP overℚ-factorial threefolds in all characteristics p>0.As a corollary,we generalise many recent results to low characteristics including:WO-rationality of klt singulariti...We show the validity of the relative dlt MMP overℚ-factorial threefolds in all characteristics p>0.As a corollary,we generalise many recent results to low characteristics including:WO-rationality of klt singularities,inversion of adjunction,and normality of divisorial centres up to a universal homeomorphism.展开更多
We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,an...We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,and show that the termination of flips for pseudo-effective NQC log canonical generalized pairs which admit NQC weak Zariski decompositions follows from the termination of flips in lower dimensions.展开更多
We study the Dirichlet problem of the n-dimensional complex Monge-Ampere equation det（uij） = F/｜z｜2a, where 0 〈 a 〈 n. This equation comes from La Nave-Tian＇s continuity approach to the Analytic Minimal Model P...We study the Dirichlet problem of the n-dimensional complex Monge-Ampere equation det（uij） = F/｜z｜2a, where 0 〈 a 〈 n. This equation comes from La Nave-Tian＇s continuity approach to the Analytic Minimal Model Program.展开更多
In our previous work,we introduced the Generalised Nonvanishing Conjecture,which generalises several central conjectures in algebraic geometry.In this paper,we derive some remarkable nonvanishing results for pluricano...In our previous work,we introduced the Generalised Nonvanishing Conjecture,which generalises several central conjectures in algebraic geometry.In this paper,we derive some remarkable nonvanishing results for pluricanonical bundles which were not predicted by the Minimal Model Program,by making progress towards the Generalised Nonvanishing Conjecture in every dimension.The main step is to establish that a somewhat stronger version of the Generalised Nonvanishing Conjecture holds almost always in the presence of metrics with generalised algebraic singularities,assuming the Minimal Model Program in lower dimensions.展开更多
文摘In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs（X, Δ） when X is a projective horospherical variety.
基金supported by NSF research Grants no.DMS-1300750,DMS-1840190,DMS-1801851 and by a grant from the Simons Foundation,Award number 256202supported by the Engineering and Physical Sciences Research Council(EP/L015234/1)during his PhD at Imperial College London+1 种基金the National Science Foundation under Grant no.DMS-1638352 at the Institute for Advanced Study in Princetonthe National Science Foundation under Grant no.DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley,California,during the Spring 2019 semester.
文摘We show the validity of the relative dlt MMP overℚ-factorial threefolds in all characteristics p>0.As a corollary,we generalise many recent results to low characteristics including:WO-rationality of klt singularities,inversion of adjunction,and normality of divisorial centres up to a universal homeomorphism.
基金supported by the China National Postdoctoral Program for Innovative Talents(Grant No.BX2021269)by the China Postdoctoral Science Foundation(Grant No.2021M702925)。
文摘We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,and show that the termination of flips for pseudo-effective NQC log canonical generalized pairs which admit NQC weak Zariski decompositions follows from the termination of flips in lower dimensions.
基金supported by NSFC(Grant No.11331001)supported by NSFC(Grant No.11501285)
文摘We study the Dirichlet problem of the n-dimensional complex Monge-Ampere equation det（uij） = F/｜z｜2a, where 0 〈 a 〈 n. This equation comes from La Nave-Tian＇s continuity approach to the Analytic Minimal Model Program.
文摘In our previous work,we introduced the Generalised Nonvanishing Conjecture,which generalises several central conjectures in algebraic geometry.In this paper,we derive some remarkable nonvanishing results for pluricanonical bundles which were not predicted by the Minimal Model Program,by making progress towards the Generalised Nonvanishing Conjecture in every dimension.The main step is to establish that a somewhat stronger version of the Generalised Nonvanishing Conjecture holds almost always in the presence of metrics with generalised algebraic singularities,assuming the Minimal Model Program in lower dimensions.
