We study in detail the degeneration of K3 to T-4/Z(2). We obtain an explicit embedding of the lattice of collapsed cycles of T-4/Z(2) into the lattice of integral cycles of K3 in two different ways. Our first method exploits the duality to the heterotic string on T-3. This allows us to describe the degeneration in terms of Wilson lines. Our second method is based on the blow-up of T-4/Z(2). From this blow-up, we directly construct the full lattice of integral cycles of K3. Finally, we use our results to describe the action of the Enriques involution on elliptic K3 surfaces, finding that a Weierstrass model description is consistent with the Enriques involution only in the F-theory limit.

Weierstrass meets Enriques

VALANDRO, ROBERTO
2010

Abstract

We study in detail the degeneration of K3 to T-4/Z(2). We obtain an explicit embedding of the lattice of collapsed cycles of T-4/Z(2) into the lattice of integral cycles of K3 in two different ways. Our first method exploits the duality to the heterotic string on T-3. This allows us to describe the degeneration in terms of Wilson lines. Our second method is based on the blow-up of T-4/Z(2). From this blow-up, we directly construct the full lattice of integral cycles of K3. Finally, we use our results to describe the action of the Enriques involution on elliptic K3 surfaces, finding that a Weierstrass model description is consistent with the Enriques involution only in the F-theory limit.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2875473
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 8
social impact