인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

Parameter spaces: constructions and examples * Basic facts about moduli spaces of curves * Techniques * Construction of M_g * Limit Linear Series and the Brill-Noether Theory * Geometry of moduli spaces: Selected Results.

Moduli of curves

Let G be an inner form of a general linear group over a non-archimedean local field. We prove that the local Langlands correspondence for G preserves depths. We also show that the local Langlands correspondence for inner forms of special linear groups preserves the depths of essentially tame Langlands parameters.

Progress in Mathematics

완효성 비료와 4종복비의 혼용 시용이 팔레놉시스의 생육에 미치는 효과

Proceedings of the American Mathematical Society

We prove a formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety as a variation on another definition of the homology Chern class of singular varieties, introduced by W. Fulton; and we discuss the relation between these classes and others, such as Mather's Chern class and the ,l-class we introduced in previous work. 0. INTRODUCTION There are several candidates for a notion of homology 'Chern class' of a (possibly singular) algebraic variety X, agreeing with the class obtained as dual of the total Chern class of the tangent bundle of X if X is nonsingular. One such notion was introduced by R. MacPherson [MacPherson], agreeing (as it was later understood) with a class introduced earlier by M.-IJ. Schwartz, and enjoying good functorial properties. A different class was defined by W. Fulton ([Fulton], 4.2.6), in a different and somewhat more general setting. The main purpose of this paper is to prove a precise relation between the Schwartz-MacPherson and the Fulton class of a hypersurface X of a nonsingular variety. We denote these two classes by csM(X), CF (X) respectively. A summary of the context and essential definitions is given in ?1, where we present several different statements of the result. The version which expresses most directly the link between the two classes mentioned above goes as follows. Fulton's class for a subscheme X of a nonsingular variety M is defined by CF(X) :m= c(TMIx) n s(X, M), that is, by capping the total Chern class of the ambient space against the Segre class of the subscheme (it is proved in [Fulton], 4.2.6 that this definition does not depend on the choice of the ambient variety M). For a hypersurface X of a nonsingular variety M, let Y be the 'singular subscheme' of X (locally defined by the partial derivatives of an equation of X). For an integer k > 0 we can consider the k-th thickening X(k) of X along Y, and then consider its Fulton class CF(X(k)). It is easily seen that CF (X(k)) is a polynomial in k (with coefficients in the Chow group A,*(X)), so it can be formally evaluated at negative k's. We can then define a class (* C*(X) :_ CF(X( 1))The main result of this paper is Theorem. c* (X) is equal to the Chern-Schwartz-MacPherson class of X. Received by the editors June 3, 1997. 1991 Mathematics Subject Classification. Prinmary 14C17, 32S60. Supported in part by NSF grant DMS-9500843. @ 1999 American Mathbemiatical Society 3989 This content downloaded from 157.55.39.136 on Thu, 01 Dec 2016 05:45:16 UTC All use subject to http://about.jstor.org/terms

/pdf/chern-classes-for-singular-hypersurfaces-2s2ime6kxu.pdf

Chern classes for singular hypersurfaces

https://www.math.fsu.edu/~aluffi/archive/paper173.pdf

Computing characteristic classes of projective schemes

We present new explicit constructions of weak coupling limits of F-theory generalizing Sen’s construction to elliptic fibrations which are not necessary given in a Weierstrass form. These new constructions allow for an elegant derivation of several brane configurations that do not occur within the original framework of Sen’s limit, or which would require complicated geometric tuning or break supersymmetry. Our approach is streamlined by first deriving a simple geometric interpretation of Sen’s weak coupling limit. This leads to a natural way of organizing all such limits in terms of transitions from semistable to unstable singular fibers. These constructions provide a new playground for model builders as they enlarge the number of supersymmetric configurations that can be constructed in F-theory. We present several explicit examples for E
 8, E
 7 and E
 6 elliptic fibrations.

/pdf/new-orientifold-weak-coupling-limits-in-f-theory-2bioxtfwcv.pdf

New orientifold weak coupling limits in F-theory

We consider the infinite family of Feynman graphs known as the “banana graphs” and compute explicitly the classes of the corresponding graph hypersurfaces in the Grothendieck ring of varieties as well as their Chern–Schwartz–MacPherson classes, using the classical Cremona transformation and the dual graph, and a blowup formula for characteristic classes. We outline the interesting similarities between these operations and we give formulae for cones obtained by simple operations on graphs. We formulate a positivity conjecture for characteristic classes of graph hypersurfaces and discuss briefly the effect of passing to noncommutative spacetime.

/pdf/feynman-motives-of-banana-graphs-3yzhhs39u4.pdf

Feynman motives of banana graphs

In this note we compare two notions of Chern class of an algebraic scheme X (over C) specializing to the Chern class of the tangent bundle c(TX) ∩ [X] when X is nonsingular. The first of such notions is MacPherson’s Chern class, defined by means of Mather-Chern classes and local Euler obstructions [5]. MacPherson’s Chern class is functorial with respect to a push-forward defined via topological Euler characteristics of fibers; in particular, mapping to a point shows that the degree of the zero-dimensional component of MacPherson’s Chern class of a complete variety X equals the Euler characteristic χ(X) of X. We denote MacPherson’s Chern class of X by cMP (X). The second notion is Fulton’s intrinsic class of schemes X ′ that can be embedded in a nonsingular variety M : Fulton shows ([3], Example 4.2.6) that the class cF (X ′) = c(TM) ∩ s(X ′,M) is independent of the choice of embedding of X ′. This class has the advantage of being defined over arbitrary fields and in a completely algebraic fashion, but does not satisfy at first sight nice functorial properties: cf. [3], p. 377. (MacPherson’s class can also be defined algebraically over any field of characteristic 0: this is done in [4].) To state our result we need to remind the reader that if W is a scheme supported on a Cartier divisor X of a nonsingular variety M , then the Segre class of W in M can be written in terms of the Segre class of X and the Segre class of the residual scheme J to X in W : for a precise statement of this fact, see [3], Proposition 9.2, or section 2 below. By modifying this expression, we can make sense of the “Segre class” in M of an object “X \J” in which J is intuitively speaking “removed” from X. Since this object has a Segre class, we can define its Fulton–Chern class as above. Here is our result:

/pdf/macpherson-s-and-fulton-s-chern-classes-of-hypersurfaces-oqpotbrikd.pdf

Paolo Aluffi

Papers

Chern classes for singular hypersurfaces

Computing characteristic classes of projective schemes

New orientifold weak coupling limits in F-theory

Feynman motives of banana graphs

MacPherson's and Fulton's Chern classes of hypersurfaces