Nested varieties of K3 type

In this paper, we study and relate Calabi-Yau subHodge structures of Fano subvarieties of different Grassmannians. In particular, we construct isomorphisms between Calabi- Yau subHodge structures of hyperplane sections of Gr(3; n) and those of other varieties arising from symplectic Grassmannians and congruences of lines or planes. We describe in details the case of the hyperplane sections of Gr(3; 10), which are Fano varieties of K3 type whose K3 Hodge structures are isomorphic with those of other Fano varieties such as the Peskine variety. These isomorphisms are obtained via the study of geometrical correspondences between different Grassmannians, such as projections and jumps via two-step flags. We also show how these correspondences allow to construct crepant categorical resolutions of the Coble cubics. Finally, we prove a generalization of Orlov's formula on semiorthogonal decompositions for blow-ups, which provides conjectural categorical counterparts of our Hodge-theoretical results

Introducing a rainfall compound distribution model based on weather patterns sub-sampling

This paper presents a probabilistic model for daily rainfall, using sub-sampling based on meteorological circulation. We classified eight typical but contrasted synoptic situations (weather patterns) for France and surrounding areas, using a "bottom-up" approach, i.e. from the shape of the rain field to the synoptic situations described by geopotential fields. These weather patterns (WP) provide a discriminating variable that is consistent with French climatology, and allows seasonal rainfall records to be split into more homogeneous sub-samples, in term of meteorological genesis. <br><br> First results show how the combination of seasonal and WP sub-sampling strongly influences the identification of the asymptotic behaviour of rainfall probabilistic models. Furthermore, with this level of stratification, an asymptotic exponential behaviour of each sub-sample appears as a reasonable hypothesis. This first part is illustrated with two daily rainfall records from SE of France. <br><br> The distribution of the multi-exponential weather patterns (MEWP) is then defined as the composition, for a given season, of all WP sub-sample marginal distributions, weighted by the relative frequency of occurrence of each WP. This model is finally compared to Exponential and Generalized Pareto distributions, showing good features in terms of robustness and accuracy. These final statistical results are computed from a wide dataset of 478 rainfall chronicles spread on the southern half of France. All these data cover the 1953–2005 period

Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi

Instanton bundles on Fano threefolds

We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in a greater detail.Comment: 31 page, to appear in CEJ

Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives

14 pagesInternational audienceMaking use of homological projective duality and the recent theory of (Jacobians of) noncommutative Chow motives, we compute the rational Chow groups of a complete intersection of either two quadrics or three odd-dimensional quadrics. We show moreover that the unique non-trivial algebraic Jacobians are the middle ones. As a first application, we describe the rational Chow motives of these complete intersections. As a second application, we prove that smooth fibrations in such complete intersections over small dimensional bases S verify Murre's conjecture (dim(S) less or equal to 1), Grothendieck's standard conjectures (dim(S) less of equal to 2), and Hodge's conjecture (dim(S) less or equal to 3)

Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives

Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when dim(S) [less than or equal to] 1), Grothendieck's standard conjecture of Lefschetz type (when dim(S) [less than or equal to] 2), and Hodge's conjecture (when dim(S) [less than or equal to] 3).National Science Foundation (U.S.) (CAREER Award #1350472)Fundação para a Ciência e a Tecnologia (Portugal) (project grant UID/MAT/00297/2013 (Centro de Matemática e Aplicações)

The use of historical information for regional frequency analysis of extreme skew surge

The design of effective coastal protections requires an adequate estimation of the annual occurrence probability of rare events associated with a return period up to 103 years. Regional frequency analysis (RFA) has been proven to be an applicable way to estimate extreme events by sorting regional data into large and spatially distributed datasets. Nowadays, historical data are available to provide new insight on past event estimation. The utilisation of historical information would increase the precision and the reliability of regional extreme's quantile estimation. However, historical data are from significant extreme events that are not recorded by tide gauge. They usually look like isolated data and they are different from continuous data from systematic measurements of tide gauges. This makes the definition of the duration of our observations period complicated. However, the duration of the observation period is crucial for the frequency estimation of extreme occurrences. For this reason, we introduced here the concept of credible duration. The proposed RFA method (hereinafter referenced as FAB, from the name of the authors) allows the use of historical data together with systematic data, which is a result of the use of the credible duration concept