By Mica Szurek, Jarosaw Wisniewski, Piotr Pragacz

This publication provides the lawsuits from the convention on algebraic geometry in honor of Professor Friedrich Hirzebruch's seventieth Birthday. the development was once held on the Stefan Banach overseas Mathematical heart in Warsaw (Poland). the subjects lined within the booklet comprise intersection concept, singularities, low-dimensional manifolds, moduli areas, quantity concept, and interactions among mathematical physics and geometry. additionally incorporated are articles from notes of 2 detailed lectures. the 1st, by means of Professor M. Atiyah, describes the real contributions to the sphere of geometry through Professor Hirzebruch. the second one article comprises notes from the debate added on the convention via Professor Hirzebruch. members to the amount are top researchers within the box

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**Additional resources for Algebraic Geometry, Hirzebruch 70: Proceedings of an Algebraic Geometry Conference in Honor of F. Hirzebruch's 70th Birthday, May 11-16, 1998, Stefan ... Mathematical**

**Example text**

An ) = Proj k[X0 , . . , Xn ], for j = i. We where the grading of the polynomial ring is given by deg Xi = ai . The sheaf OP (1) = OP (H) is a rank-one reﬂexive sheaf corresponding to a Weil divisor class H. The global sections of OP (n) = OP (nH) are the homogeneous polynomials of (weighted) degree n. The divisor class group Cl(P) is isomorphic to Z, generated by H. The divisor H is Q-Cartier, and satisﬁes H n = 1/(a0 · · · an ). 1. Moduli spaces of surfaces of general type 43 The canonical divisor class KP is given by KP = −(a0 + a1 + · · · + an )H.

Grushevsky, K. Hulek, and R. Laza. Extending the Prym map to toroidal compactiﬁcations of the moduli space of abelian varieties. Preprint, 2014. [29] S. Casalaina-Martin, D. Jensen, and R. Laza. The geometry of the ball quotient model of the moduli space of genus four curves. In Compact Moduli Spaces and Vector Bundles, volume 564 of Contemp. , pages 107–136. Amer. Math. , 2012. [30] S. Casalaina-Martin, D. Jensen, and R. Laza. Log canonical models and variation of GIT for genus 4 canonical curves.

J. Amer. Math. , 23(2):405–468, 2010. [22] C. Borcea. K3 surfaces with involution and mirror pairs of Calabi–Yau manifolds. In Mirror Symmetry, II, volume 1 of AMS/IP Stud. Adv. , pages 717–743. Amer. Math. , Providence, RI, 1997. E. Borcherds, L. Katzarkov, T. I. Shepherd-Barron. Families of K3 surfaces. J. , 7(1):183–193, 1998. [24] A. Borel. Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem. J. Diﬀerential Geometry, 6:543–560, 1972. S. C. Spencer on their sixtieth birthdays.