GEOGRAPHY OF GORENSTEIN STABLE LOG SURFACES

Feb 19, 2014 - Page 1 .... Figure 1. The geography of minimal and Gorenstein stable surfaces. Our results ... The first author was supported by the Bi...

0 downloads 5 Views 675KB Size

Recommend Documents

Nov 23, 2016 - [CD89]. Fabrizio Catanese and Olivier Debarre. Surfaces with K2 = 2, pg = 1, q = 0. .... Rick Miranda. Triple covers in algebraic geometry. Amer.

May 16, 2010 - ber of flips is bounded by the number of rational 1-contractions with projective YP/Z according to Corollary 4.5. □. Corollary 4.12. Let (Y/Z,BY ), (Y //Z, BY ) be two klt slt wlc models of general type. Then any (small) log flop (Y/

Nov 21, 2016 - arrange f2 to be of the form above by completing the square with y1 and rescaling x2. This does not affect the choices made in (4.4). As in the classical case, h0(P3,I. ϕ( ˜C). (3)) = 5, so we can find an irreducible cubic surface va

May 16, 2010 - Introduction. 1. 2. Geography of log models. 2. 3. Positive cones. 13. 4. Finiteness results for log models. 18. 5. Geography generalities. 24. 6. Linkage ... have the same wlc models and the models are numerically equivalent, that is:

Nov 24, 2013 - age of X under its Albanese map. The Albanese dimension dim a(X) can vary from one to dim X. We say X is of Albanese dimension m,.

Nov 24, 2013 - In particular, if α is the Albanese map of X, then we call. Xd the d-th ..... 4g − 4. 3 . Follow the proof of Theorem 8.1 almost verbatim. We can get.

28 Sep 2009 - In practice, the much weaker ..... some a, b the answer to one of these three questions is “yes” , the same .... exact sequences on V . If k = 1 and D1 ∈ |rH|, where H is a fixed ample ...... The key observation of this proof is t

Nov 10, 2015 - singularity of degree 4 (see case 4.6 in loc.cit.). The low degree of the branch divisors leaves very few combinatorial possibilities. We will now describe all possible normal examples where D has only ordinary singu- larities; the sur

Jan 11, 2017 - Iitaka [Iit77] proposes a program generalizing the classical theory of com- ... Basic examples are log ruled (log uniruled) log surface pairs, ..... [Miy01] Masayoshi Miyanishi, Open algebraic surfaces, CRM Monograph Series,.

May 11, 2012 - The second author discusses the X-method for klt surfaces in positive characteristic in [Ta2]. For a related topic, see also [CMM]. Theorem 2.1 (Artin, Keel). Let X be a complete normal algebraic surface defined over an algebraically c

Dec 11, 2015 - I.3.1) The skeleton. I.3.2) Skeleton and fundamental group. I.4) Ramified coverings. I.4.1) Ramified coverings and formal Riemann surfaces. I.4.2) Ramified .... systems, erased completely Riemann's original notion of Riemann surface. I

different local configurations is estimated according to their weights. Finally, a sufficient condition .... event “a local configuration whose weight is smaller than W occurs somewhere in the ball of center x and .... that x ∈ B(0,r), y ∈ δB(

Jan 16, 2018 - call it π : (Xc, ∆c + Ec) → (X, ∆). Thus −Θc ∼R,π KXc + ∆c + Ec is π-ample. In particular, Ex(π) ⊂ Supp Θc by Lemma 16. Thus π is small, Ec = 0 and π : (Xc, ∆c) → (X, ∆) is the required lc modification. Let

Introduction. Let C be a Riemann surface of genus g, let KC be a canonical divisor on C, and let D be an effective divisor on C of degree d. Two basic rational maps arise in this context, namely the linear series map: φ|KC +D| : C − −> |KC + D|â

Oct 4, 2018 - For m ≥ 0, denote by M0,m(S, β) the Deligne-Mumford moduli stacks of (isomorphism ...... [49] M. Reineke, Degenerate cohomological Hall algebra and quantized Donaldson-Thomas ... E-mail address: [email protected]

AG] 19 Nov 2003 . Q-COMPLEMENTS ON LOG SURFACES. I. YU. FEDOROV AND S. A. KUDRYAVTSEV. Introduction. In this paper the log surfaces without ...

Sep 11, 2017 - canonical bundle of an elliptic surface with section and marked fibers. .... surface canonical bundle formula (see Proposition 3.5) to elliptic ...

Sep 4, 2016 - We prove that the conjecture holds for many classes of (not ..... The following technical remark is useful for the study of the invariant c(a), which will be ...... Department of Mathematics, University of Utah, 155 South 1400 East, ...

Jul 23, 2018 - Next, suppose multp Z = 0. Then D = D(φ) is flat over p. Let Dν → D be the normalization and δ = length(ODν /OD) the delta invariant. It is easy ...

Mar 20, 2016 - Writing χ(λ1,...,λr) as χλ1···λr , the graded character of R/IF , for F as above, is. χR/IF (t) = χ4. + (χ4 + χ31)t ... it follows that graded artinian Gorenstein algebras which admit an action of Sn come in two types, whi

Dec 21, 2015 - consider arbitrary abelian categories with enough projective objects. .... The stable category of A, denoted by A, is defined to be the additive quotient ... Db (A-Mod) and Db (B-Mod) are equivalent as triangulated categories.

Jan 26, 2015 - ... Flips and abundance for algebraic threefolds, Société Mathématique de. France, Paris, 1992. Papers from the Second Summer Seminar on Algebraic Geometry held at the University of Utah, Salt Lake City, Utah, August 1991; Astérisq

Aug 2, 2009 - ... GR/R77773/01. –1– version 3.0, July 31, 2009 ... Kähler manifolds is still not completely realized, though a book by Lübke and Teleman ([LT]) ... Remark 1.3. Clearly, if dω = 0, then the Bismut connection is torsion-free, ...

Jun 14, 2016 - other hand, one can use Ross and Thomas's [11, Example 5.30] to ...... The face ∆L is generated by rL = 9 − d disjoint (−1)-curves E1,...,ErL .